I was looking at minimal combinations of material needed to force checkmate (K+R, Q+B, R+N+N, etc). You end up with a sort of threshold of how much material is needed, and that sort of assigns a strength to the king. But that made me wonder if K+K is sufficient material to force checkmate. Obviously this is normally impossible, but in the hypothetical endgame where white has two kings and black has one (and make the obvious loosenings of the restrictions on moving into check), could the two kings force checkmate against the one king?

Alternatively, one could think of it as white having a king and a fairy chess piece that moves exactly like a king. Is this enough material to force checkmate?