diff --git a/packages/inter-protocol/test/smartWallet/test-oracle-integration.js b/packages/inter-protocol/test/smartWallet/test-oracle-integration.js
index 584d50233739..52950aeb7187 100644
--- a/packages/inter-protocol/test/smartWallet/test-oracle-integration.js
+++ b/packages/inter-protocol/test/smartWallet/test-oracle-integration.js
@@ -337,7 +337,7 @@ test.serial('errors', async t => {
     }),
     {
       error: undefined,
-      numWantsSatisfied: 1,
+      numWantsSatisfied: Infinity,
     },
   );
   await eventLoopIteration();
diff --git a/packages/vats/test/bootstrapTests/test-vaults-integration.js b/packages/vats/test/bootstrapTests/test-vaults-integration.js
index 7e2bbd08ad96..0109b47168a4 100644
--- a/packages/vats/test/bootstrapTests/test-vaults-integration.js
+++ b/packages/vats/test/bootstrapTests/test-vaults-integration.js
@@ -135,7 +135,7 @@ test('adjust balances', async t => {
     updated: 'offerStatus',
     status: {
       id: 'adjust',
-      numWantsSatisfied: 1,
+      numWantsSatisfied: Infinity,
     },
   });
 });
@@ -193,7 +193,8 @@ test('close vault', async t => {
     updated: 'offerStatus',
     status: {
       id: 'close-insufficient',
-      numWantsSatisfied: 1, // trivially true because proposal `want` was empty.
+      // XXX there were no wants. Zoe treats as Infinitely satisfied
+      numWantsSatisfied: Infinity,
       error: `Error: ${message}`,
     },
   });
@@ -215,6 +216,7 @@ test('close vault', async t => {
       result: 'your vault is closed, thank you for your business',
       // funds are returned
       payouts: likePayouts(giveCollateral, 0),
+      numWantsSatisfied: Infinity,
     },
   });
 });
@@ -280,7 +282,7 @@ test('exit bid', async t => {
     status: {
       id: 'bid',
       result: 'Your bid has been accepted', // it was accepted before being exited
-      numWantsSatisfied: 1, // trivially 1 because there were no "wants" in the proposal
+      numWantsSatisfied: Infinity, // trivially, because there were no "wants" in the proposal
       payouts: {
         // got back the give
         Bid: { value: 100000n },
@@ -309,7 +311,9 @@ test('propose change to auction governance param', async t => {
   });
 
   await eventLoopIteration();
-  t.like(wd.getLatestUpdateRecord(), { status: { numWantsSatisfied: 1 } });
+  t.like(wd.getLatestUpdateRecord(), {
+    status: { numWantsSatisfied: Infinity },
+  });
 
   const auctioneer = agoricNamesRemotes.instance.auctioneer;
   const timerBrand = agoricNamesRemotes.brand.timer;
@@ -341,7 +345,9 @@ test('propose change to auction governance param', async t => {
   });
 
   await eventLoopIteration();
-  t.like(wd.getLatestUpdateRecord(), { status: { numWantsSatisfied: 1 } });
+  t.like(wd.getLatestUpdateRecord(), {
+    status: { numWantsSatisfied: Infinity },
+  });
 
   const { fromCapData } = makeMarshal(undefined, slotToBoardRemote);
   const key = `published.committees.Economic_Committee.latestQuestion`;
diff --git a/packages/wallet/api/test/test-lib-wallet.js b/packages/wallet/api/test/test-lib-wallet.js
index 7bf3569a0ce3..3886983cf586 100644
--- a/packages/wallet/api/test/test-lib-wallet.js
+++ b/packages/wallet/api/test/test-lib-wallet.js
@@ -1338,6 +1338,7 @@ test('addOffer invitationQuery', async t => {
           value: 1n,
         },
       },
+      multiples: 1n,
       exit: {
         onDemand: null,
       },
@@ -1459,6 +1460,7 @@ test('addOffer offer.invitation', async t => {
           value: 1n,
         },
       },
+      multiples: 1n,
       exit: {
         onDemand: null,
       },
diff --git a/packages/zoe/src/cleanProposal.js b/packages/zoe/src/cleanProposal.js
index 19064df6b3f6..3e15c233531a 100644
--- a/packages/zoe/src/cleanProposal.js
+++ b/packages/zoe/src/cleanProposal.js
@@ -4,9 +4,11 @@ import { assertRecord } from '@endo/marshal';
 import { assertKey, assertPattern, mustMatch, isKey } from '@agoric/store';
 import { FullProposalShape } from './typeGuards.js';
 import { arrayToObj } from './objArrayConversion.js';
+import { natSafeMath } from './contractSupport/safeMath.js';
 
 import './internal-types.js';
 
+const { values } = Object;
 const { ownKeys } = Reflect;
 
 export const MAX_KEYWORD_LENGTH = 100;
@@ -140,6 +142,7 @@ export const cleanProposal = (proposal, getAssetKindByBrand) => {
   const {
     want = harden({}),
     give = harden({}),
+    multiples = 1n,
     exit = harden({ onDemand: null }),
     ...rest
   } = proposal;
@@ -155,10 +158,36 @@ export const cleanProposal = (proposal, getAssetKindByBrand) => {
   const cleanedProposal = harden({
     want: cleanedWant,
     give: cleanedGive,
+    multiples,
     exit,
   });
   mustMatch(cleanedProposal, FullProposalShape, 'proposal');
+  if (multiples > 1n) {
+    for (const amount of values(cleanedGive)) {
+      typeof amount.value === 'bigint' ||
+        Fail`multiples > 1 not yet implemented for non-fungibles: ${multiples} * ${amount}`;
+    }
+  }
   assertExit(exit);
   assertKeywordNotInBoth(cleanedWant, cleanedGive);
   return cleanedProposal;
 };
+
+/**
+ *
+ * @param {Amount} amount
+ * @param {bigint} multiples
+ * @returns {Amount}
+ */
+export const scaleAmount = (amount, multiples) => {
+  if (multiples === 1n) {
+    return amount;
+  }
+  const { brand, value } = amount;
+  if (typeof value !== 'bigint') {
+    throw Fail`multiples > 1 not yet implemented for non-fungibles: ${multiples} * ${amount}`;
+  }
+  assert(value >= 1n);
+  return harden({ brand, value: natSafeMath.multiply(value, multiples) });
+};
+harden(scaleAmount);
diff --git a/packages/zoe/src/contractFacet/offerSafety.js b/packages/zoe/src/contractFacet/offerSafety.js
index 6171b00287d7..869817c5b55a 100644
--- a/packages/zoe/src/contractFacet/offerSafety.js
+++ b/packages/zoe/src/contractFacet/offerSafety.js
@@ -1,34 +1,51 @@
 import { AmountMath } from '@agoric/ertp';
+import { natSafeMath } from '../contractSupport/safeMath.js';
+
+const { Fail } = assert;
+const { entries } = Object;
 
 /**
- * Helper to perform satisfiesWant and satisfiesGive. Is
- * allocationAmount greater than or equal to requiredAmount for every
- * keyword of giveOrWant?
- *
- * To prepare for multiples, satisfiesWant and satisfiesGive return 0 or 1.
- * isOfferSafe will still be boolean. When we have Multiples, satisfiesWant and
- * satisfiesGive will tell how many times the offer was matched.
+ * Helper to perform numWantsSatisfied and numGivesSatisfied. How many times
+ * does the `allocation` satisfy the `giveOrWant`?
  *
  * @param {AmountKeywordRecord} giveOrWant
  * @param {AmountKeywordRecord} allocation
- * @returns {0|1}
+ * @returns {number} If the giveOrWant is empty, then any allocation satisfies
+ * it an `Infinity` number of times.
  */
-const satisfiesInternal = (giveOrWant = {}, allocation) => {
-  const isGTEByKeyword = ([keyword, requiredAmount]) => {
-    // If there is no allocation for a keyword, we know the giveOrWant
-    // is not satisfied without checking further.
+const numSatisfied = (giveOrWant = {}, allocation) => {
+  let multiples = Infinity;
+  for (const [keyword, requiredAmount] of entries(giveOrWant)) {
     if (allocation[keyword] === undefined) {
       return 0;
     }
     const allocationAmount = allocation[keyword];
-    return AmountMath.isGTE(allocationAmount, requiredAmount) ? 1 : 0;
-  };
-  return Object.entries(giveOrWant).every(isGTEByKeyword) ? 1 : 0;
+    if (!AmountMath.isGTE(allocationAmount, requiredAmount)) {
+      return 0;
+    }
+    if (typeof requiredAmount.value !== 'bigint') {
+      multiples = 1;
+    } else if (requiredAmount.value > 0n) {
+      assert.typeof(allocationAmount.value, 'bigint');
+      const howMany = natSafeMath.floorDivide(
+        allocationAmount.value,
+        requiredAmount.value,
+      );
+      if (multiples > howMany) {
+        howMany <= Number.MAX_SAFE_INTEGER ||
+          Fail`numSatisfied ${howMany} out of safe integer range`;
+        multiples = Number(howMany);
+      }
+    }
+  }
+  return multiples;
 };
 
 /**
  * For this allocation to satisfy what the user wanted, their
  * allocated amounts must be greater than or equal to proposal.want.
+ * Even if multiples > 1n, this succeeds if it satisfies just one
+ * unit of want.
  *
  * @param {ProposalRecord} proposal - the rules that accompanied the
  * escrow of payments that dictate what the user expected to get back
@@ -39,14 +56,17 @@ const satisfiesInternal = (giveOrWant = {}, allocation) => {
  * @param {AmountKeywordRecord} allocation - a record with keywords
  * as keys and amounts as values. These amounts are the reallocation
  * to be given to a user.
+ * @returns {number} If the want is empty, then any allocation satisfies
+ * it an `Infinity` number of times.
  */
-const satisfiesWant = (proposal, allocation) =>
-  satisfiesInternal(proposal.want, allocation);
+export const numWantsSatisfied = (proposal, allocation) =>
+  numSatisfied(proposal.want, allocation);
+harden(numWantsSatisfied);
 
 /**
  * For this allocation to count as a full refund, the allocated
  * amounts must be greater than or equal to what was originally
- * offered (proposal.give).
+ * offered (proposal.give * proposal.multiples).
  *
  * @param  {ProposalRecord} proposal - the rules that accompanied the
  * escrow of payments that dictate what the user expected to get back
@@ -57,9 +77,13 @@ const satisfiesWant = (proposal, allocation) =>
  * @param  {AmountKeywordRecord} allocation - a record with keywords
  * as keys and amounts as values. These amounts are the reallocation
  * to be given to a user.
+ * @returns {number} If the give is empty, then any allocation satisfies
+ * it an `Infinity` number of times.
  */
-const satisfiesGive = (proposal, allocation) =>
-  satisfiesInternal(proposal.give, allocation);
+// Commented out because not currently used
+// const numGivesSatisfied = (proposal, allocation) =>
+//   numSatisfied(proposal.give, allocation);
+// harden(numGivesSatisfied);
 
 /**
  * `isOfferSafe` checks offer safety for a single offer.
@@ -78,13 +102,10 @@ const satisfiesGive = (proposal, allocation) =>
  * as keys and amounts as values. These amounts are the reallocation
  * to be given to a user.
  */
-function isOfferSafe(proposal, allocation) {
-  return (
-    satisfiesGive(proposal, allocation) > 0 ||
-    satisfiesWant(proposal, allocation) > 0
-  );
-}
-
+export const isOfferSafe = (proposal, allocation) => {
+  const { give, want, multiples } = proposal;
+  const howMany =
+    numSatisfied(give, allocation) + numSatisfied(want, allocation);
+  return howMany >= multiples;
+};
 harden(isOfferSafe);
-harden(satisfiesWant);
-export { isOfferSafe, satisfiesWant };
diff --git a/packages/zoe/src/contractSupport/zoeHelpers.js b/packages/zoe/src/contractSupport/zoeHelpers.js
index 2287395c33fd..6884de88fc55 100644
--- a/packages/zoe/src/contractSupport/zoeHelpers.js
+++ b/packages/zoe/src/contractSupport/zoeHelpers.js
@@ -3,8 +3,8 @@ import { E } from '@endo/eventual-send';
 import { makePromiseKit } from '@endo/promise-kit';
 import { AssetKind } from '@agoric/ertp';
 import { fromUniqueEntries } from '@agoric/internal';
-import { satisfiesWant } from '../contractFacet/offerSafety.js';
 import { atomicTransfer, fromOnly, toOnly } from './atomicTransfer.js';
+import { numWantsSatisfied } from '../contractFacet/offerSafety.js';
 
 export const defaultAcceptanceMsg = `The offer has been accepted. Once the contract has been completed, please check your payout`;
 
@@ -33,20 +33,25 @@ export const assertIssuerKeywords = (zcf, expected) => {
  * check; whether the allocation constitutes a refund is not
  * checked. The update is merged with currentAllocation
  * (update's values prevailing if the keywords are the same)
- * to produce the newAllocation. The return value is 0 for
- * false and 1 for true. When multiples are introduced, any
- * positive return value will mean true.
+ * to produce the newAllocation. The return value indicates the
+ * number of times the want was satisfied.
+ *
+ * There are some calls to `satisfies` dating from when it returned a
+ * boolean rather than a number. Manual inspection verifies that these
+ * are only sensitive to whether the result is truthy or falsy.
+ * Since `0` is falsy and any positive number (including `Infinity`)
+ * is truthy, all these callers still operate correctly.
  *
  * @param {ZCF} zcf
  * @param {ZcfSeatPartial} seat
  * @param {AmountKeywordRecord} update
- * @returns {0|1}
+ * @returns {number}
  */
 export const satisfies = (zcf, seat, update) => {
   const currentAllocation = seat.getCurrentAllocation();
   const newAllocation = { ...currentAllocation, ...update };
   const proposal = seat.getProposal();
-  return satisfiesWant(proposal, newAllocation);
+  return numWantsSatisfied(proposal, newAllocation);
 };
 
 /** @type {Swap} */
@@ -160,6 +165,14 @@ export const assertProposalShape = (seat, expected) => {
   assertKeys(actual.give, expected.give);
   assertKeys(actual.want, expected.want);
   assertKeys(actual.exit, expected.exit);
+  if ('multiples' in expected) {
+    // Not sure what to do with the value of expected.multiples. Probably
+    // nothing until we convert all this to use proper patterns
+  } else {
+    // multiples other than 1n need to be opted into
+    actual.multiples === 1n ||
+      Fail`Only 1n multiples expected: ${actual.multiples}`;
+  }
 };
 
 /* Given a brand, assert that brand is AssetKind.NAT. */
diff --git a/packages/zoe/src/typeGuards.js b/packages/zoe/src/typeGuards.js
index a5264eb2e190..d8aa45703a19 100644
--- a/packages/zoe/src/typeGuards.js
+++ b/packages/zoe/src/typeGuards.js
@@ -71,6 +71,7 @@ export const TimerShape = makeHandleShape('timer');
 export const FullProposalShape = harden({
   want: AmountPatternKeywordRecordShape,
   give: AmountKeywordRecordShape,
+  multiples: M.bigint(),
   // To accept only one, we could use M.or rather than M.splitRecord,
   // but the error messages would have been worse. Rather,
   // cleanProposal's assertExit checks that there's exactly one.
diff --git a/packages/zoe/src/zoeService/escrowStorage.js b/packages/zoe/src/zoeService/escrowStorage.js
index ccb894cae6da..5f66f70212de 100644
--- a/packages/zoe/src/zoeService/escrowStorage.js
+++ b/packages/zoe/src/zoeService/escrowStorage.js
@@ -7,7 +7,7 @@ import { provideDurableWeakMapStore } from '@agoric/vat-data';
 import './types.js';
 import './internal-types.js';
 
-import { cleanKeywords } from '../cleanProposal.js';
+import { cleanKeywords, scaleAmount } from '../cleanProposal.js';
 import { arrayToObj } from '../objArrayConversion.js';
 
 /**
@@ -74,7 +74,7 @@ export const provideEscrowStorage = baggage => {
 
   /** @type {DepositPayments} */
   const depositPayments = async (proposal, payments) => {
-    const { give, want } = proposal;
+    const { give, want, multiples } = proposal;
     const giveKeywords = Object.keys(give);
     const wantKeywords = Object.keys(want);
     const paymentKeywords = cleanKeywords(payments);
@@ -108,7 +108,8 @@ export const provideEscrowStorage = baggage => {
           )} keyword in proposal.give did not have an associated payment in the paymentKeywordRecord, which had keywords: ${q(
             paymentKeywords,
           )}`;
-        return doDepositPayment(payments[keyword], give[keyword]);
+        const giveAmount = scaleAmount(give[keyword], multiples);
+        return doDepositPayment(payments[keyword], giveAmount);
       }),
     );
 
diff --git a/packages/zoe/src/zoeService/offer/offer.js b/packages/zoe/src/zoeService/offer/offer.js
index f34d578e1719..cda80b4324a4 100644
--- a/packages/zoe/src/zoeService/offer/offer.js
+++ b/packages/zoe/src/zoeService/offer/offer.js
@@ -48,7 +48,12 @@ export const makeOfferMethod = offerDataAccess => {
     const proposal = cleanProposal(uncleanProposal, getAssetKindByBrand);
     const proposalShape =
       offerDataAccess.getProposalShapeForInvitation(invitationHandle);
-    if (proposalShape !== undefined) {
+    if (proposalShape === undefined) {
+      // For the contract to opt into accepting a multiples value other than
+      // `1n`, it must provide `makeInvitation` with a proposalShape.
+      proposal.multiples === 1n ||
+        Fail`Contract not willing to accept multiples for this invitation: ${proposal}`;
+    } else {
       mustMatch(proposal, proposalShape, `${q(description)} proposal`);
     }
 
diff --git a/packages/zoe/src/zoeService/types.js b/packages/zoe/src/zoeService/types.js
index 34897fd32e34..18de08ced10a 100644
--- a/packages/zoe/src/zoeService/types.js
+++ b/packages/zoe/src/zoeService/types.js
@@ -210,11 +210,12 @@
  * interact with the contract.
  * @property {() => Promise<boolean>} hasExited
  * Returns true if the seat has exited, false if it is still active.
- * @property {() => Promise<0|1>} numWantsSatisfied returns 1 if the proposal's
- * want clause was satisfied by the final allocation, otherwise 0. This is
- * numeric to support a planned enhancement called "multiples" which will allow
- * the return value to be any non-negative number. The promise will resolve
- * after the seat has exited.
+ * @property {() => Promise<number>} numWantsSatisfied
+ * Returns the number of times that the proposal's `want` clause was satisfied
+ * by the final allocation. If the `want` was not satisfied then it was
+ * satisfied `0` times. If the want was satisfied, then it was satisfied
+ * `>= 1` times. The promise will resolve after the seat has exited.
+ *
  * @property {() => Promise<Allocation>} getFinalAllocation
  * return a promise for the final allocation. The promise will resolve after the
  * seat has exited.
@@ -227,6 +228,7 @@
  *
  * @typedef {{give: AmountKeywordRecord,
  *            want: AmountKeywordRecord,
+ *            multiples: bigint,
  *            exit: ExitRule
  *           }} ProposalRecord
  */
diff --git a/packages/zoe/src/zoeService/zoeSeat.js b/packages/zoe/src/zoeService/zoeSeat.js
index 2462440d97ec..dffd5d3ebd56 100644
--- a/packages/zoe/src/zoeService/zoeSeat.js
+++ b/packages/zoe/src/zoeService/zoeSeat.js
@@ -4,7 +4,8 @@ import { M, prepareExoClassKit } from '@agoric/vat-data';
 import { deeplyFulfilled } from '@endo/marshal';
 import { makePromiseKit } from '@endo/promise-kit';
 
-import { satisfiesWant } from '../contractFacet/offerSafety.js';
+import { numWantsSatisfied } from '../contractFacet/offerSafety.js';
+
 import '../types.js';
 import '../internal-types.js';
 import {
@@ -319,8 +320,8 @@ export const makeZoeSeatAdminFactory = baggage => {
           const { state } = this;
           return E.when(
             state.subscriber.subscribeAfter(),
-            () => satisfiesWant(state.proposal, state.currentAllocation),
-            () => satisfiesWant(state.proposal, state.currentAllocation),
+            () => numWantsSatisfied(state.proposal, state.currentAllocation),
+            () => numWantsSatisfied(state.proposal, state.currentAllocation),
           );
         },
         getExitSubscriber() {
diff --git a/packages/zoe/test/unitTests/contractSupport/test-offerTo.js b/packages/zoe/test/unitTests/contractSupport/test-offerTo.js
index 6a8f7b8d4ec3..2db9f5d43dda 100644
--- a/packages/zoe/test/unitTests/contractSupport/test-offerTo.js
+++ b/packages/zoe/test/unitTests/contractSupport/test-offerTo.js
@@ -104,7 +104,7 @@ test(`offerTo - basic usage`, async t => {
     want: {
       TokenL: moolaIssuer.getBrand().getAmountShape(),
     },
-    // multiples: 1n,
+    multiples: 1n,
     exit: {
       onDemand: null,
     },
@@ -220,7 +220,10 @@ test(`offerTo - violates offer safety of fromSeat`, async t => {
       ),
     {
       message:
-        /Offer safety was violated by the proposed allocation: {"Token[JK]":{"brand":"\[Alleged: .* brand]","value":"\[0n]"},"Token[KJ]":{"brand":"\[Alleged: .* brand]","value":"\[0n]"}}. Proposal was/,
+        // TODO golden error message list property names in sorted order,
+        // which should work again after https://github.com/endojs/endo/pull/1678
+        //
+        'Offer safety was violated by the proposed allocation: {"TokenJ":{"brand":"[Alleged: moola brand]","value":"[0n]"},"TokenK":{"brand":"[Alleged: bucks brand]","value":"[0n]"}}. Proposal was {"exit":{"onDemand":null},"give":{"TokenK":{"brand":"[Alleged: bucks brand]","value":"[5n]"}},"multiples":"[1n]","want":{"TokenJ":{"brand":"[Alleged: moola brand]","value":"[3n]"}}}',
     },
   );
 
diff --git a/packages/zoe/test/unitTests/contracts/test-priceAggregator.js b/packages/zoe/test/unitTests/contracts/test-priceAggregator.js
index 639006832210..be852994e846 100644
--- a/packages/zoe/test/unitTests/contracts/test-priceAggregator.js
+++ b/packages/zoe/test/unitTests/contracts/test-priceAggregator.js
@@ -574,7 +574,7 @@ test('oracle continuing invitation', async t => {
 
   const invPrice = await E(invitationMakers).PushPrice('1234');
   const invPriceResult = await E(zoe).offer(invPrice);
-  t.deepEqual(await E(invPriceResult).numWantsSatisfied(), 1);
+  t.deepEqual(await E(invPriceResult).numWantsSatisfied(), Infinity);
 
   await E(oracleTimer).tick();
   await E(oracleTimer).tick();
diff --git a/packages/zoe/test/unitTests/test-cleanProposal.js b/packages/zoe/test/unitTests/test-cleanProposal.js
index 2ac334bac699..c2131d86c114 100644
--- a/packages/zoe/test/unitTests/test-cleanProposal.js
+++ b/packages/zoe/test/unitTests/test-cleanProposal.js
@@ -29,6 +29,7 @@ test('cleanProposal test', t => {
     {
       give: { Asset: simoleans(1n) },
       want: { Price: moola(3n) },
+      multiples: 1n,
       exit: { onDemand: null },
     },
   );
@@ -38,6 +39,7 @@ test('cleanProposal - all empty', t => {
   proposeGood(t, {}, 'nat', {
     give: harden({}),
     want: harden({}),
+    multiples: 1n,
     exit: { onDemand: null },
   });
 
@@ -52,6 +54,7 @@ test('cleanProposal - all empty', t => {
     {
       give: harden({}),
       want: harden({}),
+      multiples: 1n,
       exit: { waived: null },
     },
   );
@@ -72,6 +75,7 @@ test('cleanProposal - repeated brands', t => {
     {
       want: { Asset2: simoleans(1n) },
       give: { Price2: moola(3n) },
+      multiples: 1n,
       exit: { afterDeadline: { timer, deadline: 100n } },
     },
   );
@@ -108,6 +112,7 @@ test('cleanProposal - want patterns', t => {
     {
       want: { Asset2: M.any() },
       give: { Price2: moola(3n) },
+      multiples: 1n,
       exit: { afterDeadline: { timer, deadline: 100n } },
     },
   );
@@ -187,9 +192,10 @@ test('cleanProposal - other wrong stuff', t => {
     /keyword "Not Ident" must be an ascii identifier starting with upper case./,
   );
   proposeGood(t, { give: { ['A'.repeat(100)]: simoleans(1n) } }, 'nat', {
-    exit: { onDemand: null },
-    give: { ['A'.repeat(100)]: simoleans(1n) },
     want: {},
+    give: { ['A'.repeat(100)]: simoleans(1n) },
+    multiples: 1n,
+    exit: { onDemand: null },
   });
   proposeBad(
     t,
diff --git a/packages/zoe/test/unitTests/test-offerSafety-multiples.js b/packages/zoe/test/unitTests/test-offerSafety-multiples.js
new file mode 100644
index 000000000000..ada1f9d7abb4
--- /dev/null
+++ b/packages/zoe/test/unitTests/test-offerSafety-multiples.js
@@ -0,0 +1,193 @@
+// @ts-check
+
+// eslint-disable-next-line import/no-extraneous-dependencies
+import { test } from '@agoric/zoe/tools/prepare-test-env-ava.js';
+
+import { isOfferSafe } from '../../src/contractFacet/offerSafety.js';
+import { setup } from './setupBasicMints.js';
+
+// Potential outcomes:
+// 1. Users can get what they wanted, get back what they gave, both, or
+// neither
+// 2. Users can either get more than, less than, or equal to what they
+//    wanted or gave
+
+// possible combinations to test:
+// more than want, more than give -> isOfferSafe() = true
+// more than want, less than give -> true
+// more than want, equal to give -> true
+// less than want, more than give -> true
+// less than want, less than give -> false
+// less than want, equal to give -> true
+// equal to want, more than give -> true
+// equal to want, less than give -> true
+// equal to want, equal to give -> true
+
+// more than want, more than give -> isOfferSafe() = true
+test('isOfferSafe - more than want, more than give', t => {
+  const { moola, simoleans, bucks } = setup();
+  const proposal = harden({
+    give: { A: moola(8n) },
+    want: { B: simoleans(6n), C: bucks(7n) },
+    multiples: 5n,
+    exit: { waived: null },
+  });
+  t.truthy(
+    isOfferSafe(
+      proposal,
+      harden({ A: moola(50n), B: simoleans(35n), C: bucks(40n) }),
+    ),
+  );
+});
+
+// more than want, less than give -> true
+test('isOfferSafe - more than want, less than give', t => {
+  const { moola, simoleans, bucks } = setup();
+  const proposal = harden({
+    give: { A: moola(8n) },
+    want: { B: simoleans(6n), C: bucks(7n) },
+    multiples: 5n,
+    exit: { waived: null },
+  });
+  t.truthy(
+    isOfferSafe(
+      proposal,
+      harden({ A: moola(1n), B: simoleans(35n), C: bucks(40n) }),
+    ),
+  );
+});
+
+// more than want, equal to give -> true
+test('isOfferSafe - more than want, equal to give', t => {
+  const { moola, simoleans, bucks } = setup();
+  const proposal = harden({
+    want: { A: moola(8n) },
+    give: { B: simoleans(6n), C: bucks(7n) },
+    multiples: 5n,
+    exit: { waived: null },
+  });
+  t.truthy(
+    isOfferSafe(
+      proposal,
+      harden({ A: moola(45n), B: simoleans(30n), C: bucks(35n) }),
+    ),
+  );
+});
+
+// less than want, more than give -> true
+test('isOfferSafe - less than want, more than give', t => {
+  const { moola, simoleans, bucks } = setup();
+  const proposal = harden({
+    want: { A: moola(8n) },
+    give: { B: simoleans(6n), C: bucks(7n) },
+    multiples: 5n,
+    exit: { waived: null },
+  });
+  t.truthy(
+    isOfferSafe(
+      proposal,
+      harden({ A: moola(7n), B: simoleans(45n), C: bucks(95n) }),
+    ),
+  );
+});
+
+// less than want, less than give -> false
+test('isOfferSafe - less than want, less than give', t => {
+  const { moola, simoleans, bucks } = setup();
+  const proposal = harden({
+    want: { A: moola(8n) },
+    give: { B: simoleans(6n), C: bucks(7n) },
+    multiples: 5n,
+    exit: { waived: null },
+  });
+  t.falsy(
+    isOfferSafe(
+      proposal,
+      harden({ A: moola(7n), B: simoleans(5n), C: bucks(6n) }),
+    ),
+  );
+});
+
+// less than want, equal to give -> true
+test('isOfferSafe - less than want, equal to give', t => {
+  const { moola, simoleans, bucks } = setup();
+  const proposal = harden({
+    want: { B: simoleans(6n) },
+    give: { A: moola(1n), C: bucks(7n) },
+    multiples: 5n,
+    exit: { waived: null },
+  });
+  t.truthy(
+    isOfferSafe(
+      proposal,
+      harden({ A: moola(5n), B: simoleans(5n), C: bucks(35n) }),
+    ),
+  );
+});
+
+// equal to want, more than give -> true
+test('isOfferSafe - equal to want, more than give', t => {
+  const { moola, simoleans, bucks } = setup();
+  const proposal = harden({
+    want: { B: simoleans(6n) },
+    give: { A: moola(1n), C: bucks(7n) },
+    multiples: 5n,
+    exit: { waived: null },
+  });
+  t.truthy(
+    isOfferSafe(
+      proposal,
+      harden({ A: moola(10n), B: simoleans(30n), C: bucks(40n) }),
+    ),
+  );
+});
+
+// equal to want, less than give -> true
+test('isOfferSafe - equal to want, less than give', t => {
+  const { moola, simoleans, bucks } = setup();
+  const proposal = harden({
+    want: { B: simoleans(6n) },
+    give: { A: moola(1n), C: bucks(7n) },
+    multiples: 5n,
+    exit: { waived: null },
+  });
+  t.truthy(
+    isOfferSafe(
+      proposal,
+      harden({ A: moola(0n), B: simoleans(30n), C: bucks(0n) }),
+    ),
+  );
+});
+
+// equal to want, equal to give -> true
+test('isOfferSafe - equal to want, equal to give', t => {
+  const { moola, simoleans, bucks } = setup();
+  const proposal = harden({
+    want: { B: simoleans(6n) },
+    give: { A: moola(1n), C: bucks(7n) },
+    multiples: 5n,
+    exit: { waived: null },
+  });
+  t.truthy(
+    isOfferSafe(
+      proposal,
+      harden({ A: moola(5n), B: simoleans(30n), C: bucks(35n) }),
+    ),
+  );
+});
+
+test('isOfferSafe - empty proposal', t => {
+  const { moola, simoleans, bucks } = setup();
+  const proposal = harden({
+    give: {},
+    want: {},
+    multiples: 5n,
+    exit: { waived: null },
+  });
+  t.truthy(
+    isOfferSafe(
+      proposal,
+      harden({ A: moola(1n), B: simoleans(6n), C: bucks(7n) }),
+    ),
+  );
+});
diff --git a/packages/zoe/test/unitTests/test-offerSafety.js b/packages/zoe/test/unitTests/test-offerSafety.js
index 3499a577f440..757bcb24f428 100644
--- a/packages/zoe/test/unitTests/test-offerSafety.js
+++ b/packages/zoe/test/unitTests/test-offerSafety.js
@@ -2,7 +2,7 @@ import { test } from '@agoric/swingset-vat/tools/prepare-test-env-ava.js';
 
 import {
   isOfferSafe,
-  satisfiesWant,
+  numWantsSatisfied,
 } from '../../src/contractFacet/offerSafety.js';
 import { setup } from './setupBasicMints.js';
 
@@ -29,12 +29,27 @@ test('isOfferSafe - more than want, more than give', t => {
   const proposal = harden({
     give: { A: moola(8n) },
     want: { B: simoleans(6n), C: bucks(7n) },
+    multiples: 1n,
     exit: { waived: null },
   });
   const amounts = harden({ A: moola(10n), B: simoleans(7n), C: bucks(8n) });
 
   t.truthy(isOfferSafe(proposal, amounts));
-  t.is(satisfiesWant(proposal, amounts), 1);
+  t.is(numWantsSatisfied(proposal, amounts), 1);
+});
+
+test('isOfferSafe - much more than want, much more than give', t => {
+  const { moola, simoleans, bucks } = setup();
+  const proposal = harden({
+    give: { A: moola(8n) },
+    want: { B: simoleans(6n), C: bucks(7n) },
+    multiples: 1n,
+    exit: { waived: null },
+  });
+  const amounts = harden({ A: moola(100n), B: simoleans(70n), C: bucks(80n) });
+
+  t.truthy(isOfferSafe(proposal, amounts));
+  t.is(numWantsSatisfied(proposal, amounts), 11);
 });
 
 // more than want, less than give -> true
@@ -43,12 +58,13 @@ test('isOfferSafe - more than want, less than give', t => {
   const proposal = harden({
     give: { A: moola(8n) },
     want: { B: simoleans(6n), C: bucks(7n) },
+    multiples: 1n,
     exit: { waived: null },
   });
   const amounts = harden({ A: moola(1n), B: simoleans(7n), C: bucks(8n) });
 
   t.truthy(isOfferSafe(proposal, amounts));
-  t.is(satisfiesWant(proposal, amounts), 1);
+  t.is(numWantsSatisfied(proposal, amounts), 1);
 });
 
 // more than want, equal to give -> true
@@ -57,12 +73,13 @@ test('isOfferSafe - more than want, equal to give', t => {
   const proposal = harden({
     want: { A: moola(8n) },
     give: { B: simoleans(6n), C: bucks(7n) },
+    multiples: 1n,
     exit: { waived: null },
   });
   const amounts = harden({ A: moola(9n), B: simoleans(6n), C: bucks(7n) });
 
   t.truthy(isOfferSafe(proposal, amounts));
-  t.is(satisfiesWant(proposal, amounts), 1);
+  t.is(numWantsSatisfied(proposal, amounts), 1);
 });
 
 // less than want, more than give -> true
@@ -71,12 +88,13 @@ test('isOfferSafe - less than want, more than give', t => {
   const proposal = harden({
     want: { A: moola(8n) },
     give: { B: simoleans(6n), C: bucks(7n) },
+    multiples: 1n,
     exit: { waived: null },
   });
   const amounts = harden({ A: moola(7n), B: simoleans(9n), C: bucks(19n) });
 
   t.truthy(isOfferSafe(proposal, amounts));
-  t.is(satisfiesWant(proposal, amounts), 0);
+  t.is(numWantsSatisfied(proposal, amounts), 0);
 });
 
 // less than want, less than give -> false
@@ -85,12 +103,13 @@ test('isOfferSafe - less than want, less than give', t => {
   const proposal = harden({
     want: { A: moola(8n) },
     give: { B: simoleans(6n), C: bucks(7n) },
+    multiples: 1n,
     exit: { waived: null },
   });
   const amounts = harden({ A: moola(7n), B: simoleans(5n), C: bucks(6n) });
 
   t.falsy(isOfferSafe(proposal, amounts));
-  t.is(satisfiesWant(proposal, amounts), 0);
+  t.is(numWantsSatisfied(proposal, amounts), 0);
 });
 
 // less than want, equal to give -> true
@@ -99,12 +118,13 @@ test('isOfferSafe - less than want, equal to give', t => {
   const proposal = harden({
     want: { B: simoleans(6n) },
     give: { A: moola(1n), C: bucks(7n) },
+    multiples: 1n,
     exit: { waived: null },
   });
   const amounts = harden({ A: moola(1n), B: simoleans(5n), C: bucks(7n) });
 
   t.truthy(isOfferSafe(proposal, amounts));
-  t.is(satisfiesWant(proposal, amounts), 0);
+  t.is(numWantsSatisfied(proposal, amounts), 0);
 });
 
 // equal to want, more than give -> true
@@ -113,12 +133,13 @@ test('isOfferSafe - equal to want, more than give', t => {
   const proposal = harden({
     want: { B: simoleans(6n) },
     give: { A: moola(1n), C: bucks(7n) },
+    multiples: 1n,
     exit: { waived: null },
   });
   const amounts = harden({ A: moola(2n), B: simoleans(6n), C: bucks(8n) });
 
   t.truthy(isOfferSafe(proposal, amounts));
-  t.is(satisfiesWant(proposal, amounts), 1);
+  t.is(numWantsSatisfied(proposal, amounts), 1);
 });
 
 // equal to want, less than give -> true
@@ -127,12 +148,13 @@ test('isOfferSafe - equal to want, less than give', t => {
   const proposal = harden({
     want: { B: simoleans(6n) },
     give: { A: moola(1n), C: bucks(7n) },
+    multiples: 1n,
     exit: { waived: null },
   });
   const amounts = harden({ A: moola(0n), B: simoleans(6n), C: bucks(0n) });
 
   t.truthy(isOfferSafe(proposal, amounts));
-  t.is(satisfiesWant(proposal, amounts), 1);
+  t.is(numWantsSatisfied(proposal, amounts), 1);
 });
 
 // equal to want, equal to give -> true
@@ -141,19 +163,25 @@ test('isOfferSafe - equal to want, equal to give', t => {
   const proposal = harden({
     want: { B: simoleans(6n) },
     give: { A: moola(1n), C: bucks(7n) },
+    multiples: 1n,
     exit: { waived: null },
   });
   const amounts = harden({ A: moola(1n), B: simoleans(6n), C: bucks(7n) });
 
   t.truthy(isOfferSafe(proposal, amounts));
-  t.is(satisfiesWant(proposal, amounts), 1);
+  t.is(numWantsSatisfied(proposal, amounts), 1);
 });
 
 test('isOfferSafe - empty proposal', t => {
   const { moola, simoleans, bucks } = setup();
-  const proposal = harden({ give: {}, want: {}, exit: { waived: null } });
+  const proposal = harden({
+    give: {},
+    want: {},
+    multiples: 1n,
+    exit: { waived: null },
+  });
   const amounts = harden({ A: moola(1n), B: simoleans(6n), C: bucks(7n) });
 
   t.truthy(isOfferSafe(proposal, amounts));
-  t.is(satisfiesWant(proposal, amounts), 1);
+  t.is(numWantsSatisfied(proposal, amounts), Infinity);
 });
diff --git a/packages/zoe/test/unitTests/zcf/test-zcf.js b/packages/zoe/test/unitTests/zcf/test-zcf.js
index e4f77c559463..e00361ed3a99 100644
--- a/packages/zoe/test/unitTests/zcf/test-zcf.js
+++ b/packages/zoe/test/unitTests/zcf/test-zcf.js
@@ -719,6 +719,7 @@ test(`zcfSeat.getProposal from zcf.makeEmptySeatKit`, async t => {
     },
     give: {},
     want: {},
+    multiples: 1n,
   });
 });
 
@@ -889,6 +890,7 @@ test(`userSeat.getProposal from zcf.makeEmptySeatKit`, async t => {
     },
     give: {},
     want: {},
+    multiples: 1n,
   });
 });
 
diff --git a/packages/zoe/test/unitTests/zoe/test-escrowStorage.js b/packages/zoe/test/unitTests/zoe/test-escrowStorage.js
index e412a2513a68..3db4cc73d84e 100644
--- a/packages/zoe/test/unitTests/zoe/test-escrowStorage.js
+++ b/packages/zoe/test/unitTests/zoe/test-escrowStorage.js
@@ -53,6 +53,7 @@ test('provideEscrowStorage', async t => {
       GameTicket: gameTicketAmount,
       Money: stableAmount,
     },
+    multiples: 1n,
     exit: {
       onDemand: null,
     },
@@ -157,6 +158,7 @@ test('payments without matching give keywords', async t => {
       GameTicket: gameTicketAmount,
       Money: stableAmount,
     },
+    multiples: 1n,
     exit: {
       onDemand: null,
     },
@@ -192,6 +194,7 @@ test(`give keywords without matching payments`, async t => {
       GameTicket: gameTicketAmount,
       Money: stableAmount,
     },
+    multiples: 1n,
     exit: {
       onDemand: null,
     },