diff --git a/Tests/images/pil123rgba_red.jpg b/Tests/images/pil123rgba_red.jpg
new file mode 100644
index 000000000..073a65436
Binary files /dev/null and b/Tests/images/pil123rgba_red.jpg differ
diff --git a/Tests/test_file_gif.py b/Tests/test_file_gif.py
index dffd1006f..f908c4413 100644
--- a/Tests/test_file_gif.py
+++ b/Tests/test_file_gif.py
@@ -997,6 +997,18 @@ def test_save_I(tmp_path):
         assert_image_equal(reloaded.convert("L"), im.convert("L"))
 
 
+def test_save_wrong_modes():
+    out = BytesIO()
+    for mode in ["CMYK"]:
+        img = Image.new(mode, (20, 20))
+        with pytest.raises(ValueError):
+            img.save(out, "GIF")
+
+    for mode in ["CMYK", "LA"]:
+        img = Image.new(mode, (20, 20))
+        img.save(out, "GIF", convert_mode=True)
+
+
 def test_getdata():
     # Test getheader/getdata against legacy values.
     # Create a 'P' image with holes in the palette.
diff --git a/Tests/test_file_jpeg.py b/Tests/test_file_jpeg.py
index 203065802..9f755e8c6 100644
--- a/Tests/test_file_jpeg.py
+++ b/Tests/test_file_jpeg.py
@@ -655,14 +655,26 @@ class TestFileJpeg:
             img = Image.new(mode, (20, 20))
             img.save(out, "JPEG")
 
-    def test_save_wrong_modes(self):
+    def test_save_wrong_modes(self, tmp_path):
         # ref https://github.com/python-pillow/Pillow/issues/2005
         out = BytesIO()
-        for mode in ["LA", "La", "RGBA", "RGBa", "P"]:
+        for mode in ["LA", "La", "RGBA", "RGBa", "P", "I"]:
             img = Image.new(mode, (20, 20))
             with pytest.raises(OSError):
                 img.save(out, "JPEG")
 
+        for mode in ["LA", "RGBA", "P", "I"]:
+            img = Image.new(mode, (20, 20))
+            img.save(out, "JPEG", convert_mode=True)
+
+        temp_file = str(tmp_path / "temp.jpg")
+        with Image.open("Tests/images/pil123rgba.png") as img:
+            img.save(temp_file, convert_mode=True, fill_color="red")
+
+        with Image.open(temp_file) as reloaded:
+            with Image.open("Tests/images/pil123rgba_red.jpg") as target:
+                assert_image_similar(reloaded, target, 4)
+
     def test_save_tiff_with_dpi(self, tmp_path):
         # Arrange
         outfile = str(tmp_path / "temp.tif")
diff --git a/Tests/test_file_png.py b/Tests/test_file_png.py
index bb2b0d119..d92634d76 100644
--- a/Tests/test_file_png.py
+++ b/Tests/test_file_png.py
@@ -238,6 +238,14 @@ class TestFilePng:
         # image has 876 transparent pixels
         assert im.getchannel("A").getcolors()[0][0] == 876
 
+    def test_save_CMYK(self):
+        out = BytesIO()
+        im = Image.new("CMYK", (20, 20))
+        with pytest.raises(IOError):
+            im.save(out, "PNG")
+
+        im.save(out, "PNG", convert_mode=True)
+
     def test_save_p_transparent_palette(self, tmp_path):
         in_file = "Tests/images/pil123p.png"
         with Image.open(in_file) as im:
diff --git a/Tests/test_file_webp.py b/Tests/test_file_webp.py
index c69e13a89..339580bde 100644
--- a/Tests/test_file_webp.py
+++ b/Tests/test_file_webp.py
@@ -15,6 +15,8 @@ from .helper import (
     skip_unless_feature,
 )
 
+from io import BytesIO
+
 try:
     from PIL import _webp
 
@@ -88,6 +90,12 @@ class TestFileWebp:
                 target = target.convert(self.rgb_mode)
             assert_image_similar(image, target, epsilon)
 
+    def test_save_convert_mode(self):
+        out = BytesIO()
+        for mode in ["CMYK", "I", "L", "LA", "P"]:
+            img = Image.new(mode, (20, 20))
+            img.save(out, "WEBP", convert_mode=True)
+
     def test_write_rgb(self, tmp_path):
         """
         Can we write a RGB mode file to webp without error?
diff --git a/Tests/test_image.py b/Tests/test_image.py
index 07cf6eb92..91ecd3c4f 100644
--- a/Tests/test_image.py
+++ b/Tests/test_image.py
@@ -7,7 +7,13 @@ import warnings
 
 import pytest
 
-from PIL import Image, ImageDraw, ImagePalette, UnidentifiedImageError
+from PIL import (
+    Image,
+    ImageDraw,
+    ImagePalette,
+    TiffImagePlugin,
+    UnidentifiedImageError,
+)
 
 from .helper import (
     assert_image_equal,
@@ -424,6 +430,14 @@ class TestImage:
         for ext in [".cur", ".icns", ".tif", ".tiff"]:
             assert ext in extensions
 
+    def test_no_convert_mode(self, tmp_path):
+        assert not hasattr(TiffImagePlugin, "_convert_mode")
+
+        temp_file = str(tmp_path / "temp.tiff")
+
+        im = hopper()
+        im.save(temp_file, convert_mode=True)
+
     def test_effect_mandelbrot(self):
         # Arrange
         size = (512, 512)
diff --git a/src/PIL/GifImagePlugin.py b/src/PIL/GifImagePlugin.py
index b798bb969..4de387509 100644
--- a/src/PIL/GifImagePlugin.py
+++ b/src/PIL/GifImagePlugin.py
@@ -1022,6 +1022,13 @@ def getdata(im, offset=(0, 0), **params):
     return fp.data
 
 
+def _convert_mode(im):
+    return {
+        'LA':'P',
+        'CMYK':'RGB'
+    }.get(im.mode)
+
+
 # --------------------------------------------------------------------
 # Registry
 
diff --git a/src/PIL/Image.py b/src/PIL/Image.py
index 2e8279583..266044d49 100644
--- a/src/PIL/Image.py
+++ b/src/PIL/Image.py
@@ -2263,10 +2263,6 @@ class Image:
         # may mutate self!
         self._ensure_mutable()
 
-        save_all = params.pop("save_all", False)
-        self.encoderinfo = params
-        self.encoderconfig = ()
-
         preinit()
 
         ext = os.path.splitext(filename)[1].lower()
@@ -2281,11 +2277,20 @@ class Image:
 
         if format.upper() not in SAVE:
             init()
-        if save_all:
+        if params.pop('save_all', False):
             save_handler = SAVE_ALL[format.upper()]
         else:
             save_handler = SAVE[format.upper()]
 
+        if params.get('convert_mode'):
+            plugin = sys.modules[save_handler.__module__]
+            converted_im = self._convert_mode(plugin, params)
+            if converted_im:
+                return converted_im.save(fp, format, **params)
+
+        self.encoderinfo = params
+        self.encoderconfig = ()
+
         created = False
         if open_fp:
             created = not os.path.exists(filename)
@@ -2310,6 +2315,37 @@ class Image:
         if open_fp:
             fp.close()
 
+    def _convert_mode(self, plugin, params):
+        if not hasattr(plugin, '_convert_mode'):
+            return
+        new_mode = plugin._convert_mode(self)
+        if self.mode == 'LA' and new_mode == 'P':
+            alpha = self.getchannel('A')
+            # Convert the image into P mode but only use 255 colors
+            # in the palette out of 256.
+            im = self.convert('L') \
+                .convert('P', palette=Palette.ADAPTIVE, colors=255)
+            # Set all pixel values below 128 to 255, and the rest to 0.
+            mask = eval(alpha, lambda px: 255 if px < 128 else 0)
+            # Paste the color of index 255 and use alpha as a mask.
+            im.paste(255, mask)
+            # The transparency index is 255.
+            im.info['transparency'] = 255
+            return im
+
+        elif self.mode == 'I':
+            im = self.point([i//256 for i in range(65536)], 'L')
+            return im.convert(new_mode) if new_mode != 'L' else im
+
+        elif self.mode in ('RGBA', 'LA') and new_mode in ('RGB', 'L'):
+            fill_color = params.get('fill_color', 'white')
+            background = new(new_mode, self.size, fill_color)
+            background.paste(self, self.getchannel('A'))
+            return background
+
+        elif new_mode:
+            return self.convert(new_mode)
+
     def seek(self, frame):
         """
         Seeks to the given frame in this sequence file. If you seek
diff --git a/src/PIL/JpegImagePlugin.py b/src/PIL/JpegImagePlugin.py
index 93741ec6e..618b9996a 100644
--- a/src/PIL/JpegImagePlugin.py
+++ b/src/PIL/JpegImagePlugin.py
@@ -819,6 +819,17 @@ def jpeg_factory(fp=None, filename=None):
     return im
 
 
+def _convert_mode(im):
+    mode = im.mode
+    if mode == 'P':
+        return 'RGBA' if 'A' in im.im.getpalettemode() else 'RGB'
+    return {
+        'RGBA':'RGB',
+        'LA':'L',
+        'I':'L'
+    }.get(mode)
+
+
 # ---------------------------------------------------------------------
 # Registry stuff
 
diff --git a/src/PIL/PngImagePlugin.py b/src/PIL/PngImagePlugin.py
index 53525e22e..740727bbb 100644
--- a/src/PIL/PngImagePlugin.py
+++ b/src/PIL/PngImagePlugin.py
@@ -1420,6 +1420,12 @@ def getchunks(im, **params):
     return fp.data
 
 
+def _convert_mode(im):
+    return {
+        'CMYK':'RGB'
+    }.get(im.mode)
+
+
 # --------------------------------------------------------------------
 # Registry
 
diff --git a/src/PIL/WebPImagePlugin.py b/src/PIL/WebPImagePlugin.py
index 7dd3f5272..d81bc99a4 100644
--- a/src/PIL/WebPImagePlugin.py
+++ b/src/PIL/WebPImagePlugin.py
@@ -344,6 +344,19 @@ def _save(im, fp, filename):
     fp.write(data)
 
 
+def _convert_mode(im):
+    mode = im.mode
+    if mode == 'P':
+        return 'RGBA' if 'A' in im.im.getpalettemode() else 'RGB'
+    return {
+        # Pillow doesn't support L modes for webp for now.
+        'L':'RGB',
+        'LA':'RGBA',
+        'I':'RGB',
+        'CMYK':'RGB'
+    }.get(mode)
+
+
 Image.register_open(WebPImageFile.format, WebPImageFile, _accept)
 if SUPPORTED:
     Image.register_save(WebPImageFile.format, _save)