diff --git a/mypy/checker.py b/mypy/checker.py
index 33ed5387554d..3e0ec4f2de95 100644
--- a/mypy/checker.py
+++ b/mypy/checker.py
@@ -1979,14 +1979,19 @@ def check_reverse_op_method(
         assert defn.info
 
         # First check for a valid signature
-        method_type = CallableType(
-            [AnyType(TypeOfAny.special_form), AnyType(TypeOfAny.special_form)],
-            [nodes.ARG_POS, nodes.ARG_POS],
-            [None, None],
-            AnyType(TypeOfAny.special_form),
-            self.named_type("builtins.function"),
-        )
-        if not is_subtype(reverse_type, method_type):
+        method_types = [
+            CallableType(
+                [AnyType(TypeOfAny.special_form)] * num_args,
+                [nodes.ARG_POS] * num_args,
+                [None] * num_args,
+                AnyType(TypeOfAny.special_form),
+                self.named_type("builtins.function"),
+            )
+            # The data model allows __rpow__ to take an optional third "modulo"
+            # argument, mirroring the ternary form of __pow__.
+            for num_args in ([2, 3] if reverse_name == "__rpow__" else [2])
+        ]
+        if not any(is_subtype(reverse_type, method_type) for method_type in method_types):
             self.msg.invalid_signature(reverse_type, context)
             return
 
diff --git a/test-data/unit/check-classes.test b/test-data/unit/check-classes.test
index 2cd43c74ebb5..75619803459a 100644
--- a/test-data/unit/check-classes.test
+++ b/test-data/unit/check-classes.test
@@ -2509,6 +2509,25 @@ class C:
 tmp/foo.pyi:3: error: Invalid signature "Callable[[B], A]"
 tmp/foo.pyi:5: error: Invalid signature "Callable[[C, Any, Any], int]"
 
+[case testReverseOperatorMethodTernaryPow]
+from foo import *
+[file foo.pyi]
+from typing import overload
+class A:
+    def __rpow__(self, other: A, modulo: A) -> A: ...
+class B:
+    @overload
+    def __rpow__(self, other: B) -> B: ...
+    @overload
+    def __rpow__(self, other: B, modulo: B) -> B: ...
+class C:
+    def __rpow__(self, other: C, modulo: C, oops: C) -> C: ...
+class D:
+    def __radd__(self, other: D, modulo: D) -> D: ...
+[out]
+tmp/foo.pyi:10: error: Invalid signature "Callable[[C, C, C, C], C]"
+tmp/foo.pyi:12: error: Invalid signature "Callable[[D, D, D], D]"
+
 [case testReverseOperatorOrderingCase1]
 class A:
     def __radd__(self, other: 'A') -> int: ...