Pfew, bughouse draughts, has anyone ever played that? Also crazyhouse draughts crossed my mind, hard to judge if those would be good games though.
You could use the same rules that Crazyhouse/Bughouse add to chess, i.e. drop captured pieces anywhere except the back rank (capturing still forced etc). Would have to try that over the board to see if it makes any sense, but it just might
Crazyhouse draughts is played a lot at youth tournaments, or at least when I competed, under the name "doorgeefdammen". As far as I remember, we only ever allowed captured pieces to be dropped on your own half of the board. It worked really well!