diff --git a/typed-racket-lib/typed-racket/base-env/base-env.rkt b/typed-racket-lib/typed-racket/base-env/base-env.rkt
index e517693a..3158a4aa 100644
--- a/typed-racket-lib/typed-racket/base-env/base-env.rkt
+++ b/typed-racket-lib/typed-racket/base-env/base-env.rkt
@@ -2595,7 +2595,9 @@
 [path-add-extension
  (cl->*
   (-> -Pathlike (Un -String -Bytes) -Path)
-  (-> -SomeSystemPathlike (Un -String -Bytes) -SomeSystemPath))]
+  (-> -Pathlike (Un -String -Bytes) (Un -String -Bytes) -Path)
+  (-> -SomeSystemPathlike (Un -String -Bytes) -SomeSystemPath)
+  (-> -SomeSystemPathlike (Un -String -Bytes) (Un -String -Bytes) -SomeSystemPath))]
 
 [path-replace-suffix
  (cl->*
diff --git a/typed-racket-test/succeed/somesystempath.rkt b/typed-racket-test/succeed/somesystempath.rkt
index e6c664ad..e7a36223 100644
--- a/typed-racket-test/succeed/somesystempath.rkt
+++ b/typed-racket-test/succeed/somesystempath.rkt
@@ -15,6 +15,8 @@
    (filename-extension p)
    (path-only long-path)
    (some-system-path->string long-path)
+   (path-add-extension p ".bak")
+   (path-add-extension p ".bak" ".")
 
    ))