I haven't used the Githzerai much in my games and have never had my players encounter their leadership structure but this is how I've assumed it works:
The Githzerai, as a chaotic yet monastic society function like an ascetic version of the Presbyterian Church. Each monastery functions as an independent Consistory in which those who have moved past the rank of novice function as a self-governing group totally independent of any jurisdiction beyond the walls of their monastery. Whenever a Consistory creates an exploratory force, sends diplomats, levies troops or sends out colonists, this new entity becomes a Consistory in its own right, fully independent of the monastery and self-governing. It can choose to carry out its mission, rejoin the monastery, join another monastery or set up a monastery of its own.
The Githzerai political order, while highly ordered functions like a kind of medieval syndicalism. From time to time, for reasons of trade, war or other large-scale collective issues it is necessary for the Githzerai consistories to form a consensual federation that temporarily delegates power in limited areas to a super-consistory comprising delegates from all the groups that choose to join it. Membership in these federations is voluntary and simultaneous, overlapping federations can exist dealing with different areas requiring coordination. There has been a long tradition of such a body that sets standards and procedures for advancing up the monastic hierarchy in the various monasteries but no more than about 60% are governed by the Zerahin Consistory and its First Abbot; smaller competing bodies exist but most of the remaining 40% of monasteries actually follow the First Abbot in most matters but are, due to local tradition or some social experiment in breach of one or more established tenets.
Although not core, I haven't found this system to be at variance with any core materials or assumptions.
