The simplest answer is they are all frenemies.

The 1st edition supplement of "Ryoko Owari Toshi" had lots of ideas to mix diferent clans to work together and also work with a private agenda. But it all depends on the kind of campaign the GM wants to work with.

The easiest way is to make them all Yoriki that have been working for the same Emerald Magistrate or other imperial authority for a time, so no presentations are needed. Even the GM can ask the players what they think of each other.

Also, by experience of having played L5R for 10 years or more, the more bizarre is the group the more interesting and fun is the game.

For anything other than an imperials game, it's just so much easier to have them almost all be one clan, and base it there; the others are either diplomats, neighbors, or on musha shugyo, or perhaps married in.