Maria Comnena, daughter of the Byzantine emperor Manuel I, becomes empress after his death. His first wife survives, so there is no second marriage to Marie of Antioch. She was married to the western prince Renier of Montferrat. Would the Greeks have accepted him as emperor? Could an emperor from the west have prevented the 4th Crusade?
Actually, if the first wife hadn't died, then Maria probably would have married her first finance, who Manuel was grooming for the Imperial throne when Marie of Antioch had a son. Manuel was going to designate the man who became Bela III of Hungary as the next Byzantine Emperor, going so far as to have the man renamed Alexius, and grant him the second place in the Empire.
So in about 1166 or 67 Alexius and Maria are married. When Manuel I dies in 1180 there is not the chaos and disorder of OTL, since there are two adults now ruling as Emperor and Empress. Alexius is able to take advantage of the Third Crusade in 1187, sending Byzantine troops to occupy Iconium following its fall to Barborossa's German Crusaders. The fall of Iconium marked the breaking of Turkish control of Anatolia, and would mark the greatest accomplishment of the Comneni Dynasty.