interesting thought just hit me……
imagine 4/5/6/etc D chess game….for this context, 4D…
4 boards, one on top of another,
moves of pieces limited to the board upon which they are placed,
when a piece is captured by the opposing side, it is placed upon any board it has not been on already in place of another piece of like rank at the original starting position of it's previous board and can only be done if another peice, regardless of alignment, does not occupy that particular space. Direct jeapordy of the peice when placed is allowed.
Kings and Queens, being there are 8 sets, one set of each alignment would be colored different than traditional B/W indicating primary target for game conclusion upon capture/elim….both peices colored differently due to unique ability to change boards at will, but only upon the same position and only if open, regardless of direct jeapordy. The primary King, of course, being the game target.
Just rambling and placing one out there for the thinkers for a little mind break :) Have fun with it if you like.