Just brainstorming...
"Culture wars".
Every clan has to pick a culture. These can be from the single player game. Nord, Vaegirs, etc. This is not the same as picking a "team". If my clan is Nord and your clan is Nord we can still fight each other.
Each culture gets different, unique bonuses.
Culture is on a sliding scale, 1 to 100. The higher your culture is, the better your unique bonus is.
Culture goes up 1 point per day.
If you interact with any culture other than your own, it goes down 4 points. Nord trades with Vaegir, both lose 4 points of culture. If ever your culture hits 0 while interacting with another culture, you will switch to their culture and start gaining points in it daily. e.g., Nord with 1 culture point trades with Vaegir who has 50 culture points -- Nord clan is now a Vaegir clan.
So you would not have a big clan splinter into several sub-clans in an effort to get multiple cultures, because swapping troops, goods, gold, etc, between them would keep undermining their culture. Eventually some dominant culture would likely emerge in which case they might as well just all be in the same clan again.
A small Nord clan that is genuinely its own clan and rarely interacts with other clans would therefore have something unique to offer: the Nord bonus. They are "true Nords" and as long as they keep their interactions with others to a minimum, they will stay that way. If some mega-clan overran them and incorporated them into a big Vaegir alliance then the Nord clan would slowly end up switching to Vaegir, losing the thing that made them different.
Maybe, for example, Nords are the best throwers and one of the top shielders. Every 20 points of Nord culture grants them +1 shield skill (in strategus battles), +10 throwing wpf and +1 PT. Or maybe only Nords can craft huscarl shields, and the higher their culture is, the cheaper they are and the faster they can make them. (Rhodoks meanwhile might be shield/spear/crossbow specialists.)
So a big clan might want a casual alliance with a small clan in order to get some useful diversity on the battlefield, but the small clan needs real separation in order to retain their Nord culture and therefore their Nord bonuses. And by retaining real separation, it might be easier to maintain real splits in the larger coalitions as any sub-clans within the group would have to maintain a large degree of independence if they wanted to maintain their separate culture.
Other cultural influences might include proximity to other fiefs, members of your clan working in a fief from another culture, bonuses for working in a fief from your own culture, etc.