diff --git a/docs/changelog.md b/docs/changelog.md
index 0b04d809..b4dcf3e9 100644
--- a/docs/changelog.md
+++ b/docs/changelog.md
@@ -9,7 +9,7 @@
   and similar functions, which previously emitted
   `inference_failure` (#636)
 - Take into account additional base classes declared in stub
-  files (fixing some false positives around `typing.IO`) (#635)
+  files (fixing some false positives around `typing.IO`) (#635, #639)
 - Fix crash on stubs that contain dict or set literals (#634)
 - Remove more old special cases and improve robustness of
   annotation parsing (#630)
diff --git a/pyanalyze/checker.py b/pyanalyze/checker.py
index 1fb095ee..61f1f4c7 100644
--- a/pyanalyze/checker.py
+++ b/pyanalyze/checker.py
@@ -164,7 +164,7 @@ def _build_type_object(self, typ: Union[type, super, str]) -> TypeObject:
             return TypeObject(typ, self.get_additional_bases(typ))
         else:
             plugin_bases = self.get_additional_bases(typ)
-            typeshed_bases = self._get_typeshed_bases(typ)
+            typeshed_bases = self._get_recursive_typeshed_bases(typ)
             additional_bases = plugin_bases | typeshed_bases
             # Is it marked as a protocol in stubs? If so, use the stub definition.
             if self.ts_finder.is_protocol(typ):
@@ -190,6 +190,22 @@ def _build_type_object(self, typ: Union[type, super, str]) -> TypeObject:
 
             return TypeObject(typ, additional_bases)
 
+    def _get_recursive_typeshed_bases(
+        self, typ: Union[type, str]
+    ) -> Set[Union[type, str]]:
+        seen = set()
+        to_do = {typ}
+        result = set()
+        while to_do:
+            typ = to_do.pop()
+            if typ in seen:
+                continue
+            bases = self._get_typeshed_bases(typ)
+            result |= bases
+            to_do |= bases
+            seen.add(typ)
+        return result
+
     def _get_typeshed_bases(self, typ: Union[type, str]) -> Set[Union[type, str]]:
         base_values = self.ts_finder.get_bases_recursively(typ)
         return {base.typ for base in base_values if isinstance(base, TypedValue)}
diff --git a/pyanalyze/test_type_object.py b/pyanalyze/test_type_object.py
index 70a5d624..f4af01df 100644
--- a/pyanalyze/test_type_object.py
+++ b/pyanalyze/test_type_object.py
@@ -404,3 +404,8 @@ def capybara():
             with open("x", "rb") as f:
                 assert_type(f, io.BufferedReader)
                 want_io(f)
+
+        def pacarana():
+            with open("x", "w+b") as f:
+                assert_type(f, io.BufferedRandom)
+                want_io(f)
diff --git a/pyanalyze/typeshed.py b/pyanalyze/typeshed.py
index f783a1ce..b3a3e8a8 100644
--- a/pyanalyze/typeshed.py
+++ b/pyanalyze/typeshed.py
@@ -361,6 +361,12 @@ def get_bases_recursively(self, typ: Union[type, str]) -> List[Value]:
         return bases
 
     def get_bases_for_fq_name(self, fq_name: str) -> Optional[List[Value]]:
+        if fq_name in (
+            "typing.Generic",
+            "typing.Protocol",
+            "typing_extensions.Protocol",
+        ):
+            return []
         info = self._get_info_for_name(fq_name)
         mod, _ = fq_name.rsplit(".", maxsplit=1)
         return self._get_bases_from_info(info, mod, fq_name)