It's probably more useful to think about ways to drive nontransitivity in games in general, rather than specifically copying RPS. That is to say, the situation where strategy A beating strategy B and B beating C does not imply that A beats C.

There's a general shape of games of skill, where at first nontransitivity between strategies increases with skill as people understand the possibilities better, up to a turning point at which the nontransitivity of strategies decreases until there is ultimately one dominant strategy.