Three D Chess Variant
Here is a fledging idea, that could take several directions for a chess variant. You may want to use 3 chess sets per side, and also change certain move patterns. The concept though is to use:
1. a cube one story high.
2. a cube two stories high.
A knight on the ground level can only attack pieces on the ground level, but the large board will also have a knight which is propped up by a cube one story high, it cannot attack pieces on the ground or on two cubes;
You could invent new pieces which could indeed impact pieces on levels one and two, but not the ground; and pieces that impact levels ground and one cube, but not the second cube height. You may also include a "master piece" which (in theory like the current queen) does impact all three tiers (ground, 1 cube high, 2 cube high);
Unlike the Star Trek episode, one is not looking at three floors which are separated, rather one is looking a mix-match of ground, then 2 cube, then 1 cube and completely intertwined mountainscape of heights. A player would need to know which "new" pieces can influence 2-3 tiers on the z-plane, and which pieces cannot; the player would need to know when to play offensively in the valley, versus on the plane, versus on the mountain.