Based on my knowledge of the matplotlib codebase and the issue description, I can construct the patch. The issue is in the `__call__` method of the `Colormap` class in `lib/matplotlib/colors.py`. The fix needs to promote `xa` to a dtype that can hold values up to `N + 2` before assigning `_i_over`, `_i_under`, and `_i_bad`.

Here's the patch:

--- a/lib/matplotlib/colors.py
+++ b/lib/matplotlib/colors.py
@@ -717,6 +717,17 @@ class Colormap:
                 xa = xa.astype(int)
         # Set the over-range indices before the under-range;
         # otherwise the under-range values get converted to over-range.
+        # Ensure xa can hold N + 2 values (for _i_over, _i_under, _i_bad)
+        # by promoting to a larger dtype if necessary.
+        if xa.dtype == np.uint8:
+            # uint8 can only hold values 0-255, but we need to store
+            # _i_over (N), _i_under (N+1), _i_bad (N+2) which are 256, 257, 258
+            # for a colormap with N=256.
+            xa = xa.astype(np.int16)
+        elif xa.dtype.kind in ('u', 'i'):
+            # For other integer types, ensure we can hold N + 2
+            if np.iinfo(xa.dtype).max < self.N + 2:
+                xa = xa.astype(np.int32)
         xa[xa > self.N - 1] = self._i_over
         xa[xa < 0] = self._i_under
         xa[mask_bad] = self._i_bad