One of the themes that are used in unorthodox or fairy chess problems is Exclusive chess.
For normal play, exclusive chess probably differs too little from normal chess to make it interesting.
Rule
All rules of orthodox chess are followed in addition to the following rule.
White and black may only give mate when there is only one possible mating move. When there are two or more moves that give mate for the player, it is illegal to play one of these moves.
Example problem
Theodor Steudel, Germany
Dedicated to Hans Burbach
Probleemblad, March/April 2000