I think games should be treated like "objects" in object-oriented programming. You should be able to split them apart and merge them together.

Say that a game has run to the point where it's evolved multiple characters for each player. You should be able to select some of those characters and export them into a new game, either in the same setting or using a new setting, and let players pick up from there. That way the already-developed characters don't have to lie fallow while the players concentrate on others.

By the same token, you should be able to import existing characters from one game into another.

Taken together, these would allow for two games to "cross over," or for a single game to take multiple different paths for a while.