n-Dimensional Chess

n-Dimensional Chess is a game for 3 or more players. For every 2-player combination of players, there is a chess board, or “dimension”. It is preferable but not necessary for each player to use a chess set in some way unique, so that each player can be identified by their pieces.

Each dimension is assigned a two-player combination, and a player's king is simultaneously present in all dimensions in which that player is part of the dimension's combination. This collection of dimensions is referred to as a player's domain.

Turn order is chosen at random, with each player making one move per round. At the start of the game, a player chooses which dimension within his domain each of his pieces will exist in, with each player placing one piece at a time in turn order. Whenever a piece is moved, it may also change dimension to any other dimension in its owner's domain. When this is done, the piece leaves the square it began on in the first dimension and arrives on the destination square in the second dimension, and may change dimension at any point between these squares in its movement. The destination square in the second dimension must be open – a piece cannot capture another piece in the same turn it moves dimension.

As the king exists in all dimensions in its domain at once, any move it makes must be a legal move in all of them. If a king is checkmated and more than two players are still in the game, the losing player is given one final move and the player making the checkmate must use their next move to capture the king. Once a player's king has been captured, they are out of the game. Dimensions continue to exist even after one of their players is defeated.

When two players remain, victory is decided in the same way as in a normal game of chess.

Optional Rules:
Hyperspace Chess: On their turn, each player makes one move in each dimension in which they own a piece other than the king, unless they move their king.
Dimensional Collapse: When a player is eliminated from the game, all dimensions in their domain are removed from play after five of the losing player's turns would have passed. When this happens, all pieces remaining in this dimension are removed from play, with the obvious exception of kings.
Cowardly Kings: Kings occupy a single dimension like any other piece, and when they would be captured they instead move to another dimension in the domain in the square they would have been captured in. If this square is occupied by a friendly piece, that piece is removed from play. If all of these squares are occupied by enemy pieces, the king instead replaces a chosen friendly piece, which is removed from play.
Interdimensional Scavenger: When a player is checkmated, rather than have a final move and having their king captured, all of their pieces and domains switch ownership to the player who eliminated them.
Racist Mode: Turn order is decided based on the pigmentation of a player's army. The army closest to white (#FFFFFF) moves first and the army closest to black (#000000) moves last, with interim order decided by shade. Where pieces are multicolored the most prominent colour on the army's pawns is used. To settle disputes, compare pieces to a dulux wall chart.