diff --git a/stdlib/_operator.pyi b/stdlib/_operator.pyi
index cb1c1bcfc4aa..ea09c97328e9 100644
--- a/stdlib/_operator.pyi
+++ b/stdlib/_operator.pyi
@@ -7,6 +7,9 @@ from typing_extensions import ParamSpec, TypeAlias, TypeIs
 
 _R = TypeVar("_R")
 _T = TypeVar("_T")
+_T_contra = TypeVar("_T_contra", contravariant=True)
+_U = TypeVar("_U")
+_U_co = TypeVar("_U_co", covariant=True)
 _T_co = TypeVar("_T_co", covariant=True)
 _K = TypeVar("_K")
 _V = TypeVar("_V")
@@ -58,15 +61,45 @@ def truth(a: object, /) -> bool: ...
 def is_(a: object, b: object, /) -> bool: ...
 def is_not(a: object, b: object, /) -> bool: ...
 def abs(a: SupportsAbs[_T], /) -> _T: ...
-def add(a: Any, b: Any, /) -> Any: ...
-def and_(a: Any, b: Any, /) -> Any: ...
+
+class _SupportsAdd(Protocol[_T_contra, _U_co]):
+    def __add__(self, other: _T_contra, /) -> _U_co: ...
+
+class _SupportsRAdd(Protocol[_T_contra, _U_co]):
+    def __radd__(self, other: _T_contra, /) -> _U_co: ...
+
+@overload
+def add(a: _SupportsAdd[_T, _U], b: _T, /) -> _U: ...
+@overload
+def add(a: _T, b: _SupportsRAdd[_T, _U], /) -> _U: ...
+
+class _SupportsAnd(Protocol[_T_contra, _U_co]):
+    def __and__(self, other: _T_contra, /) -> _U_co: ...
+
+class _SupportsRAnd(Protocol[_T_contra, _U_co]):
+    def __rand__(self, other: _T_contra, /) -> _U_co: ...
+
+@overload
+def and_(a: _SupportsAnd[_T, _U], b: _T, /) -> _U: ...
+@overload
+def and_(a: _T, b: _SupportsRAnd[_T, _U], /) -> _U: ...
 def floordiv(a: Any, b: Any, /) -> Any: ...
 def index(a: SupportsIndex, /) -> int: ...
 def inv(a: _SupportsInversion[_T_co], /) -> _T_co: ...
 def invert(a: _SupportsInversion[_T_co], /) -> _T_co: ...
 def lshift(a: Any, b: Any, /) -> Any: ...
 def mod(a: Any, b: Any, /) -> Any: ...
-def mul(a: Any, b: Any, /) -> Any: ...
+
+class _SupportsMul(Protocol[_T_contra, _U_co]):
+    def __mul__(self, other: _T_contra, /) -> _U_co: ...
+
+class _SupportsRMul(Protocol[_T_contra, _U_co]):
+    def __rmul__(self, other: _T_contra, /) -> _U_co: ...
+
+@overload
+def mul(a: _SupportsMul[_T, _U], b: _T, /) -> _U: ...
+@overload
+def mul(a: _T, b: _SupportsRMul[_T, _U], /) -> _U: ...
 def matmul(a: Any, b: Any, /) -> Any: ...
 def neg(a: _SupportsNeg[_T_co], /) -> _T_co: ...
 def or_(a: Any, b: Any, /) -> Any: ...