4 players play two completely independent games of chess perpendicularly on the same board. Some squares may have two pieces on them. This is basically a memory challenge in the style of blindfold chess, needing to remember which pieces are yours.
We can increase the difficulty further by having everyone's pieces be identically colored checkers. Checkers can be elegantly stacked where there is double occupancy. By having all checkers be the same, it obviates the need ever to extract a checker from underneath in case of double occupancy.
Or Bughouse.
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