diff --git a/django/core/files/storage/base.py b/django/core/files/storage/base.py
index f8b0e0cdc5..2728e1cd76 100644
--- a/django/core/files/storage/base.py
+++ b/django/core/files/storage/base.py
@@ -84,15 +84,7 @@ class Storage:
                 "Detected path traversal attempt in '%s'" % dir_name
             )
         validate_file_name(file_name)
-        # Extract file extensions (.txt, .jpeg, .tar.gz) from the filename
-        suffixes = pathlib.PurePath(file_name).suffixes
-        file_ext = ""
-        # Iterate backwards from the last suffix. Consider suffixes
-        # shorter than 5 characters to be part of the extension
-        for index, suffix in enumerate(suffixes[::-1]):
-            if index > 0 and len(suffix) >= 5:
-                break
-            file_ext = suffix + file_ext
+        file_ext = self.get_filename_extensions(file_name)
         file_root = file_name.removesuffix(file_ext)
         # If the filename is not available, generate an alternative
         # filename until one is available.
@@ -122,6 +114,10 @@ class Storage:
                 )
         return name
 
+    def get_filename_extensions(self, filename):
+        """Extract all extensions from the filename."""
+        return "".join(pathlib.PurePath(filename).suffixes)
+
     def generate_filename(self, filename):
         """
         Validate the filename by calling get_valid_name() and return a filename
diff --git a/tests/file_storage/tests.py b/tests/file_storage/tests.py
index 3ebeee22c1..c6b62ef0cc 100644
--- a/tests/file_storage/tests.py
+++ b/tests/file_storage/tests.py
@@ -738,11 +738,19 @@ class OverwritingStorageTests(FileStorageTests):
         self.assertEqual(stored_name, "test_l.txt")
         self.assertEqual(len(stored_name), 10)
 
-    def test_file_name_truncation_with_dotted_name(self):
+    def test_file_name_truncation_with_dotted_name_custom_strategy(self):
+        class DottedFileNameStorage(FileSystemStorage):
+            def get_filename_extensions(self, filename):
+                ext = filename.split(".")[-1]
+                return f".{ext}"
+
+        storage = DottedFileNameStorage(
+            location=self.temp_dir, base_url="/test_media_url/", allow_overwrite=True
+        )
         name = "test.long.dotted.name.txt"
         file = ContentFile(b"content")
-        stored_name = self.storage.save(name, file, max_length=10)
-        self.addCleanup(self.storage.delete, stored_name)
+        stored_name = storage.save(name, file, max_length=10)
+        self.addCleanup(storage.delete, stored_name)
         self.assertEqual(stored_name, "test.l.txt")
         self.assertEqual(len(stored_name), 10)