I have an idea for a game that would require a system to work- though I'm thinking something very simple like FUDGE, which is not only an easy system but is a free download for anyone that wants it.
I got the idea originally from the Piers Anthony "Blue Adept" series, in which there is a massive Olympics of sorts every few years. There are competitions in practically every field of human endeavor, from craft skills to athletics skills to combat skills to artistic skills to, of course, sexual skills. The world in which this occurs has a massive slave population, with a small contingent of citizens on the top of society. Winners in the Olympics can win citizenship as the ultimate prize. Even those placing lesser in the overall competition can win money and other valuable prizes. Slaves in this society aren't maltreated, just not full citizens, and are under the command/ownership of a citizen, who keeps the vast majority of the benefit of their labor.
The Olympics are a huge undertaking, and in addition to the competitions, there are relationships formed, intrigues carried out, and all sorts of other things.