The challenge (and what if) is that instead of the Crusades working as per OTL, the Papacy responds to the requests of Alexios with a much more orchestrated strategy. Any petitioner could join one of the new Holy Orders (and any ruler who sponsored them would be given some sort of reward) and partake in the Crusades. Each of these Orders would have the permission of the Pope and the Emperor to govern the territories as vassals. (Of who could be up for debate)
Would these orders be more co-operative with the Byzantine Empire?
Would they be more loyal to the Papacy?
I imagine a few myself (if we stick with the Middle Eastern Targets)
1) Co-operative with the Empire, subservient to the Emperor in Secular concerns, but the Pope in Rome in Spiritual - Catholic Holy Order Middle East

2) Co-operative but loyal in all means to the Papacy. Papacy unintentionally has created an Empire in the East.
3) Un-cooperative - more dangerous in the Empire, and builds aforementioned Empire.
What do people think? Could it happen? What would very large Catholic orders look like? How big a series of Holy Orders like this could the Christian World start up?