In Shogi, the modern Japanese game of Chess, because the pieces of the two sides are not distinguished by color, but by the way they point, it is possible for a player to re-enter captured pieces on the board. This has led to a furious tactical game in which draws are rare.
Attempts have been made to transfer this principle to Western chess. This has usually involved special pieces, either pieces of one color that sit on platforms the color of which indicates the side the piece is on, or pieces that are cylinders with an image of a piece having one color at one end, and the same piece of the opposite color at the other.
I believe that a chess variant has been proposed where one uses a second chessboard, dropping captured pieces on that board, so that on the second chessboard, the pieces belonging to White are black in color, and the pieces belonging to Black are white in color.
In the chess variant I proposed a few pages back, Spectral Realm Chess, the interior points of the chessboard form a second 7 by 7 board on which the game is also played. So, instead of having pieces travel between the two boards, as in that game, why not use the second board as the alternate board for drops?
Since the two boards are now interlaced with each other, an advantage may be gained from this arrangement by permitting some limited interaction between the two boards.
Here, then, are the rules for this variant, in so far as they vary from those of normal Chess.
Note that the King can capture a diagonally-adjacent enemy piece on the opposite board, therefore, either by jumping or by displacement, and that on the board of points, a piece belongs to White if it is a King and is white, or if it is not a King and is black, and so forth.
Allowing captures by diagonal jumps across boards allows a limited interaction between the two boards, but only allowing the King to move to the board of points, although this makes distinguishing between the two sides by color a tad more complicated, brings the other board fully into the game.
Also note that the restriction on the King's movement when in check is not the same as the one which applies in Spectral Realm Chess.
Note also that this game can be modified to produce a chess game that needs special equipment to a lesser degree than regular Chess. Instead of allowing drops of captured pieces, only allow captured Pawns to be dropped. When a Pawn is promoted, it is replaced by a captured piece of the appropriate color.
Of course, as that means to promote a Pawn of one's own color on the normal board, first one's opponent has to capture from you the piece you will promote it to, and then also one of your Pawns, and then drop that Pawn on the other board, and promote it to that piece, which you then capture. This would make promotion harder to achieve, and thus it would make the game slower, but it would be one way of not ever requiring some type of extra piece or token to represent a promoted piece.