I have a friend that keeps wanting to play a pacifist, but in D&D, a game that is almost entirely made of rules on how to kill people. This is always dissatisfying to er, and this is part of why: the desired story, of a person trying to do the right thing without violence was at odds with the baseline assumptions baked into the game (e.g., that the way the PCs achieve their goals is through violence).
I think you can radically change the story a game tells on a ludonarrative level, if you reskin the mechanics and think carefully about what those systems are doing and why. Dread and Star Crossed both use the same basic mechanics of a Jenga tower, but one is a horror game and one is a romance. but both tell a similar emotional story, of rising tension over time, though the tension takes different forms. Thinking about the feeling a system gives you and the decisions it makes you make can guide you to tell different stories with the same mechanics, but only once you have a clear idea what the mechanics set out to do. (I used Cthulhu Dark for a time travel game, and it worked great, because those two story types are pretty similar under the hood.)