Maybe with the right tweaks to how pieces move and interact, a 12D version of chess could be coherent. Here's a chess game with a measley 5 dimensions, IIRC pieces could interact with each other through time.
The tweaks, I think, would have to be substantial: see for example 3D tic-tac-toe where the objective had to be changed to “get as many three-in-rows as you can” because getting just one is trivial and the opponent has no chance.
https://store.steampowered.com/app/1349230/5D_Chess_With_Mul...
I found it overly complicated and not particularly fun but I know some people love it, YMMV.