The chess rules are pretty strict, but for some games, it may be necessary to adapt them. Here are some examples:
Allow non-valid moves explicitly, as they are done a lot in young children games.
Allow games without a king: there are a lot of small games available
playing with one bishop against 4 pawns
only pawns
only knight dropping "horse droppings" (little stones) on the squares
...
Allow games where only one party is allowed to move: move a piece with as less as possible moves to a field; or the famous knights tour.
Disable that pieces are taken: find a clean way for a piece to move to a field.
By combining those variations in one configuration, you should be able to have a chess engine that tells you if a move is "legal" (in that context) or not. Using an engine like that, you could support many more games than the standard one. It would even be possible to allow Chess960 just by having that additional castling rule as variation.