Twelve Dimensional Chess is Stupid (2018) (gilgamath.com)

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.

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.