diff --git a/mypy/checker.py b/mypy/checker.py
index db229e274ab7..851f23185f4f 100644
--- a/mypy/checker.py
+++ b/mypy/checker.py
@@ -1838,6 +1838,7 @@ def visit_class_def(self, defn: ClassDef) -> None:
                 if base.is_enum and base.fullname not in ENUM_BASES:
                     self.check_final_enum(defn, base)
             self.check_enum_bases(defn)
+            self.check_enum_new(defn)
 
     def check_final_deletable(self, typ: TypeInfo) -> None:
         # These checks are only for mypyc. Only perform some checks that are easier
@@ -1934,9 +1935,8 @@ def is_final_enum_value(self, sym: SymbolTableNode) -> bool:
 
     def check_enum_bases(self, defn: ClassDef) -> None:
         enum_base: Optional[Instance] = None
-        data_base: Optional[Instance] = None
         for base in defn.info.bases:
-            if enum_base is None and base.type.fullname in ENUM_BASES:
+            if enum_base is None and base.type.is_enum:
                 enum_base = base
                 continue
             elif enum_base is not None:
@@ -1946,23 +1946,36 @@ def check_enum_bases(self, defn: ClassDef) -> None:
                 )
                 break
 
-            # This might not be 100% correct, because runtime `__new__`
-            # and `__new__` from `typeshed` are sometimes different,
-            # but it is good enough.
-            new_method = base.type.get('__new__')
-            if (data_base is None
-                    and enum_base is None  # data type is always before `Enum`
-                    and new_method
-                    and new_method.node
-                    and new_method.node.fullname != 'builtins.object.__new__'):
-                data_base = base
-                continue
-            elif data_base is not None:
+    def check_enum_new(self, defn: ClassDef) -> None:
+        def has_new_method(info: TypeInfo) -> bool:
+            new_method = info.get('__new__')
+            return bool(
+                new_method
+                and new_method.node
+                and new_method.node.fullname != 'builtins.object.__new__'
+            )
+
+        has_new = False
+        for base in defn.info.bases:
+            candidate = False
+
+            if base.type.is_enum:
+                # If we have an `Enum`, then we need to check all its bases.
+                candidate = any(
+                    not b.is_enum and has_new_method(b)
+                    for b in base.type.mro[1:-1]
+                )
+            else:
+                candidate = has_new_method(base.type)
+
+            if candidate and has_new:
                 self.fail(
                     'Only a single data type mixin is allowed for Enum subtypes, '
                     'found extra "{}"'.format(base),
                     defn,
                 )
+            elif candidate:
+                has_new = True
 
     def check_protocol_variance(self, defn: ClassDef) -> None:
         """Check that protocol definition is compatible with declared
diff --git a/test-data/unit/check-enum.test b/test-data/unit/check-enum.test
index e1dec9aec86f..78460909cd6a 100644
--- a/test-data/unit/check-enum.test
+++ b/test-data/unit/check-enum.test
@@ -1905,6 +1905,9 @@ class Mixin:
 
 # Correct Enums:
 
+class Correct0(enum.Enum):
+    pass
+
 class Correct1(Mixin, First, enum.Enum):
     pass
 
@@ -1917,8 +1920,29 @@ class Correct3(Mixin, enum.Enum):
 class RegularClass(Mixin, First, Second):
     pass
 
+# Correct inheritance:
+
+class _InheritingDataAndMixin(Correct1):
+    pass
+
+class _CorrectWithData(First, Correct0):
+    pass
+
+class _CorrectWithDataAndMixin(Mixin, First, Correct0):
+    pass
+
+class _CorrectWithMixin(Mixin, Correct2):
+    pass
+
 # Wrong Enums:
 
+class TwoDataTypesViaInheritance(Second, Correct2):  # E: Only a single data type mixin is allowed for Enum subtypes, found extra "__main__.Correct2"
+    pass
+
+class TwoDataTypesViaInheritanceAndMixin(Second, Correct2, Mixin):  # E: No base classes are allowed after "__main__.Correct2" \
+                                                                    # E: Only a single data type mixin is allowed for Enum subtypes, found extra "__main__.Correct2"
+    pass
+
 class MixinAfterEnum1(enum.Enum, Mixin):  # E: No base classes are allowed after "enum.Enum"
     pass
 
@@ -1928,27 +1952,56 @@ class MixinAfterEnum2(First, enum.Enum, Mixin):  # E: No base classes are allowe
 class TwoDataTypes(First, Second, enum.Enum):  # E: Only a single data type mixin is allowed for Enum subtypes, found extra "__main__.Second"
     pass
 
-class TwoDataTypesAndIntEnumMixin(First, Second, enum.IntEnum, Mixin):  # E: Only a single data type mixin is allowed for Enum subtypes, found extra "__main__.Second" \
-                                                                        # E: No base classes are allowed after "enum.IntEnum"
+class TwoDataTypesAndIntEnumMixin(First, Second, enum.IntEnum, Mixin):  # E: No base classes are allowed after "enum.IntEnum" \
+                                                                        # E: Only a single data type mixin is allowed for Enum subtypes, found extra "__main__.Second"
     pass
 
 class ThreeDataTypes(First, Second, Third, enum.Enum):  # E: Only a single data type mixin is allowed for Enum subtypes, found extra "__main__.Second" \
-                                                        # E: # E: Only a single data type mixin is allowed for Enum subtypes, found extra "__main__.Third"
+                                                        # E: Only a single data type mixin is allowed for Enum subtypes, found extra "__main__.Third"
     pass
 
-class ThreeDataTypesAndMixin(First, Second, Third, enum.Enum, Mixin): # E: Only a single data type mixin is allowed for Enum subtypes, found extra "__main__.Second" \
-                                                        # E: # E: Only a single data type mixin is allowed for Enum subtypes, found extra "__main__.Third" \
-                                                        # E: No base classes are allowed after "enum.Enum"
+class ThreeDataTypesAndMixin(First, Second, Third, enum.Enum, Mixin):  # E: No base classes are allowed after "enum.Enum" \
+                                                                       # E: Only a single data type mixin is allowed for Enum subtypes, found extra "__main__.Second" \
+                                                                       # E: Only a single data type mixin is allowed for Enum subtypes, found extra "__main__.Third"
     pass
 
-class FromEnumAndOther1(Correct2, Second, enum.Enum):  # E: Only a single data type mixin is allowed for Enum subtypes, found extra "__main__.Second"
+class FromEnumAndOther1(Correct2, Second, enum.Enum):  # E: No base classes are allowed after "__main__.Correct2" \
+                                                       # E: Only a single data type mixin is allowed for Enum subtypes, found extra "__main__.Second"
     pass
 
-class FromEnumAndOther2(Correct2, Second):  # E: Only a single data type mixin is allowed for Enum subtypes, found extra "__main__.Second"
+class FromEnumAndOther2(Correct2, Second):  # E: No base classes are allowed after "__main__.Correct2" \
+                                            # E: Only a single data type mixin is allowed for Enum subtypes, found extra "__main__.Second"
     pass
 [builtins fixtures/tuple.pyi]
 
-[case testEnumtValueUnionSimplification]
+[case testRegression12258]
+from enum import Enum
+
+class MyEnum(Enum): ...
+
+class BytesEnum(bytes, MyEnum): ...  # Should be ok
+[builtins fixtures/tuple.pyi]
+
+[case testEnumWithNewHierarchy]
+import enum
+
+class A:
+    def __new__(cls, val): ...
+class B(A):
+    def __new__(cls, val): ...
+class C:
+    def __new__(cls, val): ...
+
+class E1(A, enum.Enum): ...
+class E2(B, enum.Enum): ...
+
+# Errors:
+
+class W1(C, E1): ...  # E: Only a single data type mixin is allowed for Enum subtypes, found extra "__main__.E1"
+class W2(C, E2): ...  # E: Only a single data type mixin is allowed for Enum subtypes, found extra "__main__.E2"
+[builtins fixtures/tuple.pyi]
+
+[case testEnumValueUnionSimplification]
 from enum import IntEnum
 from typing import Any