Bughouse variant: When you decide to drop a partner's captured piece on your board as your move, you choose the piece, but your opponent chooses the square it's placed on.
This would be a three step process:
1. On your turn, you choose a piece to drop.
2. Your opponent chooses any legal square on which to drop it (no illegal positions allowed; i.e. they can't check their own king, nor drop a pawn on the 1st or 8th rank).
3. You can optionally make a legal move with your dropped piece, or you can leave it be; this ends your turn either way.
This could add strategic depth amd a little more risk to the reinforcement tactic. The opponent will naturally want to place your piece on a square that gives them the best advantage, the most probable location being a square where they can capture your piece with no harm to their position. That's where the optional move comes in. It can act as more of a deterrent than a remedy. Therefore the opponent may think it best to drop your piece in a mutually 'safe' square.
This variation would cut down on the wild tactic of dropping a new pawn one square ahead of promotion.
Overall I think this rule change would make a Bughouse game more 'tricksy' and less about recycling pieces to bring about a quick mating attack from out of nowhere.