3d ChessBoard

To build this piece is very simple.
It consists of 3 planes, one of them is the lower part with no holes on them. The columns are attached on the sides and smaller columns are put inside the columns to attach all the planes together.
No glues required.
Chess is a game Strategy.
It is limited to 2 opposite players, black and white only. Each player owns the same number of attackers in opposite sites and symmetrically. Both players attack with one move at each round. Once the player has placed the piece, you cannot go backwards. Players have the same attacking pieces so its pure strategy, it does not rely on luck and overpower unit.
It plays on a 2d grid like surface.
What if the players can break this surface and jump from surface to surface?
Will it work?
I saw that this idea was done way before in this Star Trek chess edition. But I did not like since there was no physical relation between each surface. Players grab and pull the piece outside and put it back the other layer