Honestly, in my opinion it greatly destabilized the Byzantine Empire. You had crusaders sacking Constantinople, an act so shocking that the pope firmly disavowed the Fourth Crusade. If you want the Byzantine Empire to remain stable, maybe get rid of the Venetian Doge who lead the Fourth Crusade: Enrico Dandalo. Oh and the Byzantine imperial pretender who caused all of the Fourth Crusade in the first place by promising to pay crusaders if they would just depose the Byzantine government, but I cannot remember his name at the moment.
