I occasionally think it might be fun to play a chess variant that is exactly the same as regular chess, except that it is permitted to capture your own pieces as well as your opponent's pieces - so, for example, if your king was alone on the back rank with some pawns in front of it, and your opponent moved a rook or queen to the back rank and that attacking piece could not be legally captured (which would be checkmate in normal chess), it might be possible in such a variant to escape checkmate if the king could "capture" one of it's own pawns in front of it. In the way I imagine this variant, "friendly" pieces captured in this way would be removed from play permanently, just as an opponent's piece would be - so (in this example), you've jettisoned some of your own material (which is now gone for good), but at least you were able to save yourself from checkmate...
I can imagine other scenarios where it might also be useful to give up some of your own material by "capturing" it like this, in support of the greater good....
Is this a known chess variant, does it have a name that people might recognize? I've tried searching around and haven't been able to locate any discussions of a variant like this - but I can't be the first person to think about this.
Just as full disclosure, the only variant I really know anything about is bughouse, I'm not familiar with other variants, so I'm not sure I'm even Google searching for the right words...