Your challenge, should you choose to accept it, is to rework the untenable political situation of the Dual Monarchy - POD is no later or earlier than 1900.
The most natural POD would be a decicive CP victory in WWI. Bolshewiks take over Russia and Habsburg propaganda successfully promotes the (BTW likely correct) idea that whoever seperates from Austria would immediately be conquered by the Sowjets, out from the frying pan into the fire.
None of that gives a permanent solution, but it gives the Habsburgs enough air to take a deep breath and find one. That could be a greater Ausgleich were AH is turned into a confederation whose borders that are more or less drawn according to the ethnic majorities.
That should be enough to give Austria the level of stability of OTL European Union: Far from a perfect union, but a broad consensus that staying in is the lesser evil.