Monks were prolific copiers, scribblers, and writers so I would expect that they would leave some record of the internal workings of their monasteries. I am aware that break away orders would form due to ideological differences (Benedictines -> Cistercians, for instance). I want to know if we have records of similar political splits within individual monasteries. Would they compete to try to get one of their own appointed abbot? Would they recruit like-minded men to their monastery?
There's a lot of places we can find this sort of thing, hagiographies, chronicles, letters, and so on. Sometimes this is explicit, generally powerful people made enemies and sometimes those enemies wrote books, especially during periods where reform was a major concern such as the late 11th-early 12th century. Often you have to read between the lines (or at least what's obvious in the lines to a modern reader), noticing familial ties, picking up on hints that St. So-and-So may not have departed his home monastery on his own accord. The best single source is, I think, The Chronicle of Bury St. Edmund's, which provides some great insight into the operation of a powerful Benedictine monastery in the exact period you're talking about.
Antonio Sennis, a senior lecturer at University College London, delivered a 'lunchtime lecture' a couple of months ago which is directly relevant to this question. If you can put up with the incessant pacing then it's worth a listen.