So, what if the 1853 assassination attempt on Franz Josef had been pulled off successfully and thus his younger brother Maximillian takes the throne? I've always felt Maximillian was better suited to Austrian political life than he was to Mexican politics.
On the one hand I tend to think the value of his liberalism is overstated in talk about Mexico, but it's probably going to be atleast a calming influence on Austro-Hungarian politics for awhile. His brothers murder by a hungarian nationalist is probably going to put a kibosh on a compromise for a little while longer, but I still think he could probably effectively manage de-escalate the situation in the next few years.