Each player has one piece off the board, that can be switched every turn with one of his pieces but not the king. By Peter Aronson. Turning chess . Pieces can turn after movement 45 degrees. By Ralph Betza.
Knights can make some double moves.
Twins chess . Rooks, knights, and bishops are twins and move together. U Ubi-ubi chess . Experimental variant with powerfull knights. A rather different, but well known game, played with a usual chess set.