Ascanio have proposed a chess set for four players, time ago, with pieces designed as the Bauhaus chess.
This is the 4 armies chess set received by Ascanio.
The .zip file contains the objects and the chessboard in .obj format, so you can use them with any 3D software.
It is necessary to import every single piece, place it on the chessboard and apply the desired color, it is a bit laborious, but for those who have a habit of using 3D software there is no difficulty.
The rules of the game are similar to those of the game for two players, but the pawn can move forward, backward and sideways by 1 square, catching the opponent with the diagonal movement.
This rule basically modifies the classic game.
The king is not checked and the king can be captured, therefore the player is excluded from the game and the lost pieces still on the board become the property of the player who captured the king. With this rule, a player could also have three armies.
When there are only two players, the check is declared to the opposing king, the game ends with the checkmate.
Two further rules suggested by Ascanio:
Alliances can be made, but not declared.
The alliance can be betrayed.