This will probably bore the pants off of everyone, but I've done that before and I'll do it again! My current project, Outremer, is alt history based on the Crusader states surviving until the mid 16th century - the same time frame as OHMAS. Like OHMAS, Outremer is a Blood Games II game. The point of departure for Outremer occurs during the Second Crusade:
The history of Outremer is the same as ours up until the Second Crusade. Edessa had fallen to Zengi of Damascus, who died soon after, and was succeeded by his son Nur ad Din. Conrad of Germany and Louis of France set out on Crusade with the object of retaking Edessa, Louis with his young and fetching wife Eleanor of Aquitaine, who had a suit of armor made for her. Conrad, as in the real world, set off overland to avoid Roger of Sicily, with whom he was feuding, was betrayed by the Byzantines, and the German army was destroyed. Unlike in our timeline, Louis went by sea, as he and Roger were on good terms, with Roger helping him out. Louis landed in Alexandrette, and went over the mountains to Turbessel, where Jocelin II, Count of Edessa retained a rump state.
From there, they attack the Syrians in the county, drawing down the army of Nur ad Din for a battle in front of Saruj, where Louis is killed. The army, led by Jocelin and Eleanor, retreats in good order to Bile, where Nur ad Din assaults them again. This time, however, inspired by Eleanor, the Franks crush the Syrians, and Nur ad Din is killed, along with Jocelin. The army marches into Edessa and restores the state, with Eleanor as Princess of the new Principality, which owes no fealty to Byzantium.
This removes Nur ad Din, who never takes Egypt, which is thus still Shi'ite. Saladin, the son of one of Nur ad Din's generals, has only Damascus and Aleppo for resources, instead of an empire with Egypt and the Hejaz. Eleanor marries Henry II of England, but their son Richard is eventually Prince of Edessa.
Instead of the third crusade happening, Baldwin IV, the leper king, did not die in 1185 - leprosy is a disease which does not kill you, but opens you to opportunistic infections which do eventually kill you, so he could have died any time - and was alive when Saladin took Tiberias in 1187, after the death of his young nephew and heir Baldwin V. His army was defeated but not crushed - because he wasn't an idiot like King Guy in our timeline - and Baldwin was able to retreat to Caesarea, where he was beseiged. He sent messengers to Tripoli, Antioch, and Edessa, but Saladin took Jerusalem and all the rest of the kingdom.
Richard marched an army south from Edessa, joining forces with the Prince of Antioch and the Count of Tripoli, and marched to the relief of Caesarea. He took back the northern coast of the kingdom down to Haifa, with an epic seige of Acre, suffering all the while from Muslim attacks on his flank. From Haifa, he broke the seige of Caesarea, and with Baldwin, set off for Jerusalem. The armies under Richard and Baldwin broke through into Jerusalem, but were unable to oust Saladin's men from the city. After a long and fruitless battle in the city, both parties agreed to a peace. Saladin's younger brother was to marry Richard's sister, and become heir to the Kingdom of Jerusalem when Baldwin, without heirs and a leper, died. Richard retained the northern coast as a separate and independent duchy, ruled from Acre. The Kingdom was to be both Christian and Muslim - that is, without favoritism - with the royal family Muslim. The thing was done. During the third Crusade, Richard did offer his sister in marriage to Saladin's brother, but Saladin did not think he was serious, apparently.
In Outremer, Baldwin IV ruled Jerusalem for four more years before dying in 1192. Saladin was assassinated in Damascus in 1190. At the same time, the Assassins took Homs and carved out a state between Damascus and Aleppo, breaking them apart while Saladin's sucessors squabbled. Richard's father Henry II died in 1189, and Richard became King of England. He had three sons. The eldest, Henry, became Prince of Wales. The second, Bohemund, was Prince of Edessa, and the third, Baldwin, Duke of Acre.
There is more, but this is the essential difference, the key point. By retaking Edessa and removing Nur ad Din, Saladin had a much smaller army, with fewer resources. Nur ad Din never took Egypt and overthrew the Fatimid Caliphate. The states of Outremer are able to play off the Sunni Caliphate in Baghdad against the Shi'ite Fatimid Caliphate in Egypt and the Assassins in Homs. The Assassins, who were Ismaili Muslims, separate Damascus from Aleppo, and play the Christian and Muslim states against each other.
So why am I setting this 350 years later? Because I am more comfortable with Renaissance than Medieval times for one, but also to give the setting a chance to stew and mature. What was raw in 1190 becomes smooth in 1560. Religious changes have time to foster and spread. Those 350 years were not peaceful and serene, far from it! There are always low grade wars, crises, rebellions, political machinations, and strange stuff galore - there are four more more states that come into being during this time - but there is also a modus vivendi, a working relationship with shifting alliances, which makes for a wonderful renaissance stew.