^ I've thought of an idea where, say, China industrializes under the Ming (yes, a trope), and a Chinese trading company builds a Dutch or Portuguese-style maritime empire across the maritime Silk Road. That company reaches Europe and uses its superior gunboats and divide-and-rule tactics to dominate Europe's trade. A sense of European nationalism emerges, happily supported by the Vatican, which sees it as a way to suppress the Protestant heresy.
After several decades of yet more war, all of Europe that was loyal to Rome in 1054 is united under a single, Catholic Emperor, who generally has a hands-off policy towards Europe's pre-existing Kings, Dukes, Princes, etc. Britain and Scandinavia remain the last redoubts of the Protestant heresy. There are large Protestant minorities in northern Germany, Muslim minorities in southern Spain, and Jewish minorities everywhere. They all face varying levels of discrimination, and the largest reason they're tolerated at all is because the Chinese trading company demanded it to facilitate their trading activities.
After several more decades, a *fascist ideology emerges, that is mixed with a previously obscure Christian end-times prophecy to turn the Empire as insane as 1930s Japan. It then simultaneously declares war on the Protestant heretics, the Orthodox schismatics, the Saracen infidels, and the Chinese pagans. It is then reduced to rubble. The victorious Allied powers (in reality, just the Chinese, as all the other powers were also ruined) then reluctantly agree to retain the monarchy as well as a thoroughly reformed official Roman church under a democratic system.
So we have a single, predominately Catholic Empire in Europe which is a cross between OTL India and Japan, whose official language at the imperial level is Latin, but other languages are official at more local levels. But it faces plenty of social and economic problems...