Stats or PC qualities being generated for you

In at least one version or Paranoia, states are generated by your neighbors who will assign positive and negative stats. I forget which version, I think the card based one. It's fun to embed that pvp mindset in the game early on.

Shooting the Moon is about a romantic triangle, meaning live interest A and B take opposite qualities.

The Cypher system people did put out a weird west book, sounds like a decent fit. Though honestly I think most any generic system would work pretty ok.