In the Star Fleet Technical Manual (Franz Joseph, Ballantine Books, 1975), there are plans and rules for the Star Trek original series "Tridimensional Chess":

There are three main boards, each 4x4, staggered above each other so two rows of squares are superposed between any two consecutive boards. Square colours match between superposed squares (ie the middle board's black squares are above the lower board's black squares). The middle board is the neutral field, the top one Black's defending board, and the lower one White's defending board. In addition, each player has two movable attack boards, 2x2, which start attached to each player's two back corners. These boards can be attached to any of the twelve corners of the three main boards, either above or below, thus 24 positions.

The players start with King, Queen, two Bishops, two Knights, two Rooks and eight pawns. Their respective point values are 0, 9, 3, 3, 5 and 1. Black's starting arrangement (N are Kinghts) is:

P P P P two back rows of defending board
N B B N
P P P P the two movable boards
R K Q R

The moves are as in normal Chess except the 3D transposition is also taken into account. For example, a Knight can move down one board, then forward two squares (going down two boards isn't possible because the top and bottom boards aren't superposed). The adjacency of the attack boards isn't clearly defined either, but since the attachment points are near the outer corner of the corner squares, I suppose the attack board's inner square is considered above/below the attachment square.

Attack boards can be moved instead of a piece, by one adjacent position (adjacency isn't defined clearly in the text, unfortunately). This can be done only if empty or when a lone Pawn is on the attack board. A loaded attack board cannot be inverted, thus limiting its movement. Attack board movement is a pure translation --no rotation allowed.

I'll scan the images in and create a separate boardgamegeek entry when I get a chance.