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!
There is a good crossover between draughts and chess called "Altai shatra" where dropping pieces from specific board zone (i. e., fortress) is possible. The board and rules may appear complicated at the first sight, but, in fact, the game is very simple. There are two variants of it: with chess pieces (except knights) and with pawns / checkers (which can be crowned into chess queen) and chess king. Because in this game a pawn is able to do both orthogonal and diagonal captures, "Altai shatra" can be mastered easily for those who practice Frisian draughts.
As well, there are tower draughts variants where piece "reanimation" is possible. On 8x8 board it is often played according to Russian capturing rules (see en.wikipedia.org/wiki/Bashni and a video youtu.be/iD_ChvZSLO0 ), but on 10x10 it could be played according to International rules and / or Frisian rules.