So far, these pieces never control the square they occupy. I have invented the following piece to do so.
The Avenger. Moves like a knight, but when captured, is replaced by a checker, and the enemy piece placed on top. On the player's (owning the captured Avenger) turn (any turn, not necessarily the following), the player has the option of removing the checker (unless his/her own piece occupies it). If an enemy piece is on the checker, that piece is also removed from the board. This takes the turn. The checker does not move. 6 points.
Note that it is illegal for the enemy king to move onto the checker, as that would be moving into check.
Here's some perverse yet hot ideas for new piece powers. Stuff that I've toyed with in the past and then tired of after like a day:
There's more stuff too. Most of it's probably listed in some old 'Vampire Chess' thread, if that's a search you want to make.