Here's an idea. Breaking the rules of a game makes for a better game experience.
Games have rules. Some have few, others have dozens. It doesn't matter if it is a rule that tells you to roll this dice at this time in RPG, or a one that tells you how to move your piece in a board game, or even a equation that limits how high can you jump in a video game. Without those rules there would be no real game to speak of. It would be more of an experience than game. On the other hand, what would it be, if you had rules that everyone has to follow, but each person is allowed to "cheat" in some way? I would call it an awesome game experience.
Let me tell you about two games that you probably never heard about: Monastyr and Neuroshima.
The interesting thing about those systems is that during character creation you are basically choosing two ways of how to "cheat". You choose your birthplace (i.e what country/settlement you are from) and what have you been doing throughout your life (basically a professional background - a soldier or a monk). With each choice you gain a special ability that basically breaks the rules of the game in some way.
Plenty of other games have special abilities that you can get. D&D has feats, Savage Worlds has Edges, heck, even fate has...what-you-call-them... stunts. But for whatever reason they do not feel the same. Edges, Feats and Stunts don't feel unique and as fun as the "cheats" from Monastyr and Neuroshima. They feel mundane, as a player you expect to have them, they are part of your character build, not something special.
Cosmic Encounter or Apocalypse World on the RPG side of gaming. Both those games are popular because of their game altering abilities. Each player can do something that changes the flow of the game. That's not all, both of those games reinforce exclusivity of those "cheats". If you have one alien, or playbook, no one else can have the same (not as true in AW, but it would be like that with a limited number of players). You, as a player, are the only owner of this particular game breaking cheat. You can do something unique that no one else can and that makes it cool.
When I released my 24h game HEIST_ACES one piece of feedback that I got over and over again is to include unique abilities. Now I know why and will work on implementing that in the future. Saying that, I feel that many games can benefit from "cheats" like that. Give each player a special ability or two that can break the standard set of rules in one way or the other and see how much more they will enjoy their character. It will make the games more memorable for the player when they get to use their one of a kind ability. You will vividly remember when you saved the day, because you were the only person who was immune to toxic fumes. Being able to occasional break the rules like that, changes the game into more of an experience. And it's only a good thing.