Can a commander with partner have a second commander that shares a color identity?

The Partner mechanic (CR 702.124) allows a player to designate two legendary creatures as their commanders, provided both have partner (or a compatible variant like "Partner with [name]"). The only deck-building restriction this creates is that your deck's color identity is the union of both commanders' color identities (CR 903.4).

Nowhere in the Commander rules or CR 702.124 is there a requirement that the two partners have different colors. They can overlap freely — two partners can both be blue-red, or one can be a subset of the other (e.g., one mono-red and one red-green).

The color identity of your deck simply becomes the combined set of colors from both commanders. For example, if you pair Rograkh, Son of Rohgahh (colorless/red) with Thrasios, Triton Hero (blue-green), your deck's color identity is red, blue, and green. No conflict arises from any overlap.

As a concrete example: pairing Akiri, Line-Slinger (red-white) with Bruse Tarl, Boorish Herder (red-white) is perfectly legal. Both share red and white, but that is irrelevant — your deck's color identity is simply red and white.

In summary, shared colors between partner commanders are completely allowed. The only requirements are that both creatures have partner and are legendary (CR 702.124a, 903.3).