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Thank you, Larry, for the kind words. So once again we meet over a Parton variant [a fine place to meet, in my opinion.] At least this time I know it's a Parton variant. :) I can only hope posting this one works as well as posting the last one did. It, too, needs playtesting.

The problem of the slippery king in higher dimensional chess is one I've enjoyed working on for a while, although not at first. When I first realized just how slippery the higher-D king is, didn't know how many years of frustration would ensue until, with help, I finally got somewhere. I, too, am curious about just how the king gets checkmated. Certainly my previous solution cannot be employed here; it would be just wrong, very wrong to prevent a king in Alice from moving off the board it's on. But I think the number and right mix of pieces might just suffice for 3D. Don't know how well it would work out in 4D, although I have some ideas for specific pieces to deal with that, too, in case you were thinking of Directed Alice Cubed. 

The key to mate here might be in the ability of inclusive compound pieces to change boards twice in a move. This gives these pieces a greater range and flexibility than 'normal' Alice pieces. For example, they can step 1 square, move to a specific board, then leap 2 squares and return to the board on which the move started. Or they could use that ability to dodge around obstacles on more than one board, although that might be a relatively rare occurrence. Heh, playtesters wanted.