I have never seen a variant like that, it looks really weird.
Take your own pieces variation?
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I've moved this topic to the "General Chess Discussion" forum where it got a bit more interest:
http://www.chess.com/forum/view/general/quottake-your-own-piecesquot-chess-variant
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Is there a variant of chess in which you can take your own pieces?
EDIT: I've just realized my example below is flawed because of course the Black king can escape checkmate by taking his own pawn (... Kxg6/Kxh6)! I guess this would always make it very difficult to trap the king (probably why I've never heard of this variation). It would be a good handicap for one side though ...