diff --git a/core/src/main/scala-2/cats/syntax/MonadOps.scala b/core/src/main/scala-2/cats/syntax/MonadOps.scala
index 04897be36c..cc2b782378 100644
--- a/core/src/main/scala-2/cats/syntax/MonadOps.scala
+++ b/core/src/main/scala-2/cats/syntax/MonadOps.scala
@@ -30,4 +30,6 @@ final class MonadOps[F[_], A](private val fa: F[A]) extends AnyVal {
   def untilM_(p: F[Boolean])(implicit M: Monad[F]): F[Unit] = M.untilM_(fa)(p)
   def iterateWhile(p: A => Boolean)(implicit M: Monad[F]): F[A] = M.iterateWhile(fa)(p)
   def iterateUntil(p: A => Boolean)(implicit M: Monad[F]): F[A] = M.iterateUntil(fa)(p)
+  def flatMapOrKeep[A1 >: A](pfa: PartialFunction[A, F[A1]])(implicit M: Monad[F]): F[A1] =
+    M.flatMapOrKeep[A, A1](fa)(pfa)
 }
diff --git a/core/src/main/scala-3/cats/syntax/MonadOps.scala b/core/src/main/scala-3/cats/syntax/MonadOps.scala
index ef3e285bf4..7924b01b34 100644
--- a/core/src/main/scala-3/cats/syntax/MonadOps.scala
+++ b/core/src/main/scala-3/cats/syntax/MonadOps.scala
@@ -30,4 +30,6 @@ final class MonadOps[F[_], A](private val fa: F[A]) extends AnyVal {
   def untilM_(using M: Monad[F])(p: F[Boolean]): F[Unit] = M.untilM_(fa)(p)
   def iterateWhile(using M: Monad[F])(p: A => Boolean): F[A] = M.iterateWhile(fa)(p)
   def iterateUntil(using M: Monad[F])(p: A => Boolean): F[A] = M.iterateUntil(fa)(p)
+  def flatMapOrKeep[A1 >: A](using M: Monad[F])(pfa: PartialFunction[A, F[A1]]): F[A1] =
+    M.flatMapOrKeep[A, A1](fa)(pfa)
 }
diff --git a/core/src/main/scala/cats/Monad.scala b/core/src/main/scala/cats/Monad.scala
index c212fc7038..c694f854e3 100644
--- a/core/src/main/scala/cats/Monad.scala
+++ b/core/src/main/scala/cats/Monad.scala
@@ -161,6 +161,20 @@ trait Monad[F[_]] extends FlatMap[F] with Applicative[F] {
 
     tailRecM(branches.toList)(step)
   }
+
+  /**
+   * Modifies the `A` value in `F[A]` with the supplied function, if the function is defined for the value.
+   * Example:
+   * {{{
+   * scala> import cats.syntax.all._
+   *
+   * scala> List(1, 2, 3).flatMapOrKeep{ case 2 => List(2, 22, 222) }
+   * res0: List[Int] = List(1, 2, 22, 222, 3)
+   * }}}
+   */
+  def flatMapOrKeep[A, A1 >: A](fa: F[A])(pfa: PartialFunction[A, F[A1]]): F[A1] =
+    flatMap(fa)(a => pfa.applyOrElse(a, pure[A1]))
+
 }
 
 object Monad {
diff --git a/laws/src/main/scala/cats/laws/MonadLaws.scala b/laws/src/main/scala/cats/laws/MonadLaws.scala
index 3ed6ad15ed..38ca928247 100644
--- a/laws/src/main/scala/cats/laws/MonadLaws.scala
+++ b/laws/src/main/scala/cats/laws/MonadLaws.scala
@@ -57,6 +57,12 @@ trait MonadLaws[F[_]] extends ApplicativeLaws[F] with FlatMapLaws[F] {
   def mapFlatMapCoherence[A, B](fa: F[A], f: A => B): IsEq[F[B]] =
     fa.flatMap(a => F.pure(f(a))) <-> fa.map(f)
 
+  /**
+   * Make sure that flatMapOrKeep and flatMap are consistent.
+   */
+  def flatMapOrKeepToFlatMapCoherence[A, A1 >: A](fa: F[A], pfa: PartialFunction[A, F[A1]]): IsEq[F[A1]] =
+    F.flatMapOrKeep[A, A1](fa)(pfa) <-> F.flatMap(fa)(a => pfa.applyOrElse(a, F.pure[A1]))
+
   lazy val tailRecMStackSafety: IsEq[F[Int]] = {
     val n = 50000
     val res = F.tailRecM(0)(i => F.pure(if (i < n) Either.left(i + 1) else Either.right(i)))
diff --git a/laws/src/main/scala/cats/laws/discipline/MonadTests.scala b/laws/src/main/scala/cats/laws/discipline/MonadTests.scala
index bd7a2451e5..0bb727bd0d 100644
--- a/laws/src/main/scala/cats/laws/discipline/MonadTests.scala
+++ b/laws/src/main/scala/cats/laws/discipline/MonadTests.scala
@@ -55,7 +55,8 @@ trait MonadTests[F[_]] extends ApplicativeTests[F] with FlatMapTests[F] {
         Seq(
           "monad left identity" -> forAll(laws.monadLeftIdentity[A, B] _),
           "monad right identity" -> forAll(laws.monadRightIdentity[A] _),
-          "map flatMap coherence" -> forAll(laws.mapFlatMapCoherence[A, B] _)
+          "map flatMap coherence" -> forAll(laws.mapFlatMapCoherence[A, B] _),
+          "flatMapOrKeep flatMap coherence" -> forAll(laws.flatMapOrKeepToFlatMapCoherence[A, A] _)
         ) ++ (if (Platform.isJvm) Seq[(String, Prop)]("tailRecM stack safety" -> Prop.lzy(laws.tailRecMStackSafety))
               else Seq.empty)
     }
@@ -84,7 +85,8 @@ trait MonadTests[F[_]] extends ApplicativeTests[F] with FlatMapTests[F] {
         Seq(
           "monad left identity" -> forAll(laws.monadLeftIdentity[A, B] _),
           "monad right identity" -> forAll(laws.monadRightIdentity[A] _),
-          "map flatMap coherence" -> forAll(laws.mapFlatMapCoherence[A, B] _)
+          "map flatMap coherence" -> forAll(laws.mapFlatMapCoherence[A, B] _),
+          "flatMapOrKeep flatMap coherence" -> forAll(laws.flatMapOrKeepToFlatMapCoherence[A, A] _)
         )
     }
 }