diff --git a/Tests/test_file_gif.py b/Tests/test_file_gif.py
index 2632ab7c0..56da68d60 100644
--- a/Tests/test_file_gif.py
+++ b/Tests/test_file_gif.py
@@ -821,6 +821,29 @@ def test_palette_save_P(tmp_path):
         assert_image_equal(reloaded, im)
 
 
+def test_palette_save_all_P(tmp_path):
+    frames = []
+    colors = ((255, 0, 0), (0, 255, 0))
+    for color in colors:
+        frame = Image.new("P", (100, 100))
+        frame.putpalette(color)
+        frames.append(frame)
+
+    out = str(tmp_path / "temp.gif")
+    frames[0].save(
+        out, save_all=True, palette=[255, 0, 0, 0, 255, 0], append_images=frames[1:]
+    )
+
+    with Image.open(out) as im:
+        # Assert that the frames are correct, and each frame has the same palette
+        assert_image_equal(im.convert("RGB"), frames[0].convert("RGB"))
+        assert im.palette.palette == im.global_palette.palette
+
+        im.seek(1)
+        assert_image_equal(im.convert("RGB"), frames[1].convert("RGB"))
+        assert im.palette.palette == im.global_palette.palette
+
+
 def test_palette_save_ImagePalette(tmp_path):
     # Pass in a different palette, as an ImagePalette.ImagePalette
     # effectively the same as test_palette_save_P
diff --git a/src/PIL/GifImagePlugin.py b/src/PIL/GifImagePlugin.py
index fe57e24e2..efcdbd5e3 100644
--- a/src/PIL/GifImagePlugin.py
+++ b/src/PIL/GifImagePlugin.py
@@ -414,9 +414,26 @@ def _normalize_palette(im, palette, info):
             source_palette = bytearray(i // 3 for i in range(768))
         im.palette = ImagePalette.ImagePalette("RGB", palette=source_palette)
 
-    used_palette_colors = _get_optimize(im, info)
-    if used_palette_colors is not None:
-        return im.remap_palette(used_palette_colors, source_palette)
+    if palette:
+        used_palette_colors = []
+        for i in range(0, len(source_palette), 3):
+            source_color = tuple(source_palette[i : i + 3])
+            try:
+                index = im.palette.colors[source_color]
+            except KeyError:
+                index = None
+            used_palette_colors.append(index)
+        for i, index in enumerate(used_palette_colors):
+            if index is None:
+                for j in range(len(used_palette_colors)):
+                    if j not in used_palette_colors:
+                        used_palette_colors[i] = j
+                        break
+        im = im.remap_palette(used_palette_colors)
+    else:
+        used_palette_colors = _get_optimize(im, info)
+        if used_palette_colors is not None:
+            return im.remap_palette(used_palette_colors, source_palette)
 
     im.palette.palette = source_palette
     return im
@@ -507,7 +524,8 @@ def _write_multiple_frames(im, fp, palette):
                 offset = (0, 0)
             else:
                 # compress difference
-                frame_data["encoderinfo"]["include_color_table"] = True
+                if not palette:
+                    frame_data["encoderinfo"]["include_color_table"] = True
 
                 im_frame = im_frame.crop(frame_data["bbox"])
                 offset = frame_data["bbox"][:2]