The Byzantines lose the Battle of Manzikert as they did historically, but manage to get their act together a few years earlier than IOTL, after the Turks have penetrated deep into Asia Minor but (just) before the Byzantine situation becomes irrevocable. Consequently the Byzantines are able to retake the central Anatolian plateau, but at a heavy cost: the Empire's manpower and treasury are left drained, and the Imperial heartland is left devastated by years of warfare. When the Seljuk Sultanate starts to show signs of splitting apart, Emperor *Alexius recognises that this is a golden opportunity to counterattack against his Empire's enemies, and to avenge the years of trouble Byzantium had in fighting them off -- but he also recognises that his realm still hasn't fully recovered from the Anatolian wars. Accordingly he sends a message to the Pope, asking if he could possibly send a few mercenaries to help the Empire in its campaign against the heathen. Pope Urban instead preaches a Crusade as he did IOTL, and the noblemen of Europe soon start heading off east, on an armed pilgrimage to the city of Jerusalem.
So, how do people think things will develop from here? The Byzantine Empire ITTL hasn't yet recovered from Manzikert and its aftermath, but it's still in a much stronger position than it was IOTL. With the Empire in a better state to aid the Crusaders, I think the Crusade would be at least as successful as it was in real life, so Antioch, Jerusalem etc. would still be captured. Would the Byzantines then be in a position to force the Crusader States to recognise Byzantine overlordship, in fact as well as in name? And what effect would this have on the subsequent history of the region? Would, e.g., a Christian reconquest of Egypt and North Africa be on the cards? And would Byzantium be able to survive up until the present day? Any ideas and suggestions are welcome!