diff --git a/stdlib/enum.pyi b/stdlib/enum.pyi
index 9ebeba37ab71..37d90443ef68 100644
--- a/stdlib/enum.pyi
+++ b/stdlib/enum.pyi
@@ -1,6 +1,6 @@
 import sys
 import types
-from _typeshed import Self
+from _typeshed import Self, SupportsKeysAndGetItem
 from abc import ABCMeta
 from builtins import property as _builtins_property
 from collections.abc import Iterable, Iterator, Mapping
@@ -68,6 +68,16 @@ if sys.version_info >= (3, 11):
 class _EnumDict(dict[str, Any]):
     def __init__(self) -> None: ...
     def __setitem__(self, key: str, value: Any) -> None: ...
+    if sys.version_info >= (3, 11):
+        # See comment above `typing.MutableMapping.update`
+        # for why overloads are preferable to a Union here
+        #
+        # Unlike with MutableMapping.update(), the first argument is required,
+        # hence the type: ignore
+        @overload  # type: ignore[override]
+        def update(self, members: SupportsKeysAndGetItem[str, Any], **more_members: Any) -> None: ...
+        @overload
+        def update(self, members: Iterable[tuple[str, Any]], **more_members: Any) -> None: ...
 
 # Note: EnumMeta actually subclasses type directly, not ABCMeta.
 # This is a temporary workaround to allow multiple creation of enums with builtins
@@ -213,15 +223,21 @@ class Flag(Enum):
     def __and__(self: Self, other: Self) -> Self: ...
     def __xor__(self: Self, other: Self) -> Self: ...
     def __invert__(self: Self) -> Self: ...
+    if sys.version_info >= (3, 11):
+        def __iter__(self: Self) -> Iterator[Self]: ...
+        def __len__(self) -> int: ...
+        __ror__ = __or__
+        __rand__ = __and__
+        __rxor__ = __xor__
 
 class IntFlag(int, Flag):
     def __new__(cls: type[Self], value: int) -> Self: ...
     def __or__(self: Self, other: int) -> Self: ...
     def __and__(self: Self, other: int) -> Self: ...
     def __xor__(self: Self, other: int) -> Self: ...
-    def __ror__(self: Self, other: int) -> Self: ...
-    def __rand__(self: Self, other: int) -> Self: ...
-    def __rxor__(self: Self, other: int) -> Self: ...
+    __ror__ = __or__
+    __rand__ = __and__
+    __rxor__ = __xor__
 
 if sys.version_info >= (3, 11):
     class StrEnum(str, ReprEnum):
diff --git a/tests/stubtest_allowlists/py311.txt b/tests/stubtest_allowlists/py311.txt
index 72919d32c1e2..c02a30f5c5b7 100644
--- a/tests/stubtest_allowlists/py311.txt
+++ b/tests/stubtest_allowlists/py311.txt
@@ -70,20 +70,14 @@ distutils.dist.DistributionMetadata.set_platforms
 distutils.util.get_host_platform
 enum.Enum.__init__
 enum.Enum._generate_next_value_
-enum.Flag.__iter__
-enum.Flag.__len__
-enum.Flag.__rand__
-enum.Flag.__ror__
-enum.Flag.__rxor__
-enum.StrEnum.value
-enum._EnumDict.update
+enum.StrEnum.value  # read-only property at runtime but too magical for stubtest
 fractions.Fraction.__int__
 fractions.Fraction.__new__  # overload is too complicated for stubtest to resolve
 ftplib.FTP.trust_server_pasv_ipv4_address
 functools.partial.__vectorcalloffset__
 gettext.install
 hmac.new  # Stub is a white lie; see comments in the stub
-http.HTTPMethod.description
+http.HTTPMethod.description  # mutable instance attribute at runtime but we pretend it's a property
 http.server.SimpleHTTPRequestHandler.__init__  # *args is expanded
 imp.get_frozen_object
 importlib.resources.Resource