There is something that I've been thinking about - but I would have to sit down and play around on the exact setup and such - but lets called it:

Choice Cheversi

The choice is that before the game starts, you decide which set of pieces you want to play with. (and you will not know your opponents set until after you start - or possible keep it hidden and learn 1 piece at a time as they play)

For example, let say there are 4 sets to choose from.

1. (power) - 1 Queen, 2 Rooks, 1 bishop, 1 knight
2. (mid-power) - 1 queen, 2 bishop, 2 knight, 1 king
3. (mid-bulk) - 2 rook, 2 bishop, 1 knight, 1 king, 1 pawn
4. (bulk) - 1 rook, 2 bishop, 2 knight, 1 king, 2 pawn

So it would be a game of power vs. quantity - you can choose a few powerful pieces - or a more less powerful pieces to help block the power play.

AGAIN - the above is just off the top of my head - I would have to sit down, try to figure out the "strength" of each piece in the game to come up with a good set of pieces. But as you can tell - if you have "power" pieces, you have less moves - and if you choose more bulk, you will have more moves - in which you can block the power pieces