On 27 October 1169, a huge fleet of 230 Byzantine warships sailed towards the Egyptian coast, making landfall at the city of Damietta at the head of the Nile. The ships were carrying an invasion force, including heavy cavalry on 60 specially built transports.
At the same time, a large Crusader army led by the King of Jerusalem, Amalric I, marched down the coast of Sinai towards the city. The allies intended to conquer Fatimid Egypt, dividing it between them with Byzantine emperor Manuel I Komnenos taking the coastal area and Amalric's Crusaders taking the interior.
So far, everything is OTL.
Egypt was seen as the fulcrum on which the fortunes of the entire cosmic battle between Christianity and Islam would revolve. If Egypt joined forces with Nur ad Din in Syria, the Crusaders would have a serious problem. Meanwhile, the Byzantines saw the Crusader presence as a useful bulwark in the struggle against the Turks.
What happened next is the subject of some dispute. What we know is that the joint expedition failed, with the consequence that Saladin took power in Egypt in 1171. By 1187, Jerusalem was back in Muslim hands, the Crusader power had been fatally broken, and the Byzantine Empire slipped into terminal decline.
But what if the invasion of October 1169 had succeeded?
1). Could the Crusaders have survived longer than OTL?
2). Would the Byzantines have benefitted?
3). How would the Muslim world react to the loss of Egypt?
4). Could the allies have held the territory?