There are many variations included in the manual. Here are some additional ones:

Colour Chess – Tournament Setup

In order to minimise any colour advantage, the board is set randomly but with the following preparation:

Each player takes 5 of each colour tile, plus 2 additional tiles (totalling 4 additional tiles between the two players; these should all be different colours). Note that it helps for setting up subsequent games if one player has white-backed tiles, while the other has black-backed.

Each player takes their 32 tiles and randomly places them one at a time into their side of the board in a snake-like fashion, starting at their bottom left corner. (Shuffle your tiles together face-down or draw from a bag). If you pull out the final piece of any one colour before you have finished your first two rows, put it back in the bag (this is to ensure you have at least one of each colour in your 3rd and 4th row). 

This will ensure a near equal distribution of colours, but give each player a slight dominance on two of the colours.

Bughouse Colour Chess

Bughouse is a great way of playing traditional Chess with 4 players and it works with Colour Chess too (you’ll need two sets).

The rules are exactly the same (read them here), except that you can only drop in captured pieces on the second half of your turn. The colour you drop them onto must be a legal colour choice, as though you were moving to that colour; the opponent then copies that colour as usual.

Stacking Chess / Colour Chess

Plays the same as traditional Chess, except that you are allowed to move your own pieces on top of each other. Can be played on either a traditional or a coloured board.

Once stacked, only the top piece may make a move. If an opponent piece moves onto a stack of yours, only the top piece is captured; the rest remain trapped underneath until the top piece moves away.

You can either play so that players are allowed to remind themselves of what the obscured pieces in the stacks are, or so that once they are covered players must remember what is underneath.

Stacking can be added as an option to other game modes, for example you could play Sequence Colour Chess with the addition of stacking.

Reveal Chess (Action Tiles)

Randomly lay out a Chess board with the coloured side of the tiles face-down.

Play regular Chess with action tiles, but the difference is that after each player’s piece move, they must flip an unoccupied non-coloured tile. The revealed tile’s action properties will now take effect.

You must choose carefully where you want to reveal tiles and weigh up the risks of what might be revealed!

Atomic Colour Chess

Any piece that captures another destroys itself in the process, as well as any non-pawn pieces that are in the surrounding spaces.

The exception to this is the King (which is an adjustment to the normal Atomic Chess rules), who can capture without exploding itself.

This also works well with Swarm!

You can read more about Atomic Chess here.