If you mean the Great Holy Grail War I would say no. There is no real splinter factions as much as there are suddenly more candidates from the grail from families whom have either died out long ago supposedly and contrary to the current situation. This resulted in fourteen individual magi appearing for the chance to contest for the grail and being able to summon different servants of the same class aka two sabers, two archers, etc. This resulted the mage association to force a new resolution. They would split the groups up into teams, or try to get them to forge their own alliances in order to lessen the all out brawl that would certainly happen. People who don't want to ally can do so...but at the cost at being outnumbered by servants who do team up.
I will go into how this happened in story, and why exactly it transpired the way it did. As it stands this may well lead to a similar event like Apocrypha.
