If you want it to feel close to the original game, you could start with chess itself and do something that adds or removes restrictions to or from the core mechanics. Examples:
- Let players position their pieces before the match, possibly taking turns and being able to see each other's choices
- Allow limited customization of how many of which piece a player can have
- Remove the restriction on pieces moving through each other
- Add something like the "king" mechanic in checkers to allow pieces to gain or change movement options
- Have board size variations to fundamentally change the game without changing the rules
- Instead of removing a piece from the board, switch its owner and put it where the piece that took it was