Here's something I've been playing around with, possibly as a plane for Alterverse. Here, there was never a Genghis Khan; the Mongols never united, and the Shahdom of Khwarizim blossomed into a mecca of learning and culture on par with Umayyad Spain. With no united Mongol presence, the Jin Chinese Empire never falls, and goes on to become the major power in the East. The Song are still in control in the south, and the Dual Empires are bitter enemies.
In the west, Saladin's Ayyubid Caliphate remains in place in Egypt and controls the Arabian peninsula as well. To conquer Muslim affluence, the Holy Roman Empire has evolved into a true empire - no longer is the Pope a major player in the political arena. In fact, religion overall is a much less-heated subject than in OTL. With greater prosperity in the middle east comes less need for expansion into Europe. For the last century or so, cultural exchanges between the Christian and Muslim worlds have been growing and there is a cautious camaraderie developing. In this world, the great enemy is looking more and more to be the Jin Empire.