The ideal situation would be to create a unitary Empire in which all subjects have equal status; that way minorities in one region can appeal to others outside it for protection of their rights.
Could there have been an approach whereby considerably smaller and more numerous regions, based on historical entities, are created with some meaningful local autonomy, subject to the overall federal governance of a Grand Imperial Diet/administration? Neither Austria nor Hungary would exist as separate kingdoms, nor Bohemia nor Croatia; each is subdivided into counties or duchies or whatever, each with their own local administration and councils--Kreis or whatever. None would be nearly big enough to contemplate going it alone; each would have their own ethnic balance of power, sometimes being essentially a big majority of one (German, Magyar, Czech, Moravian, whatever) but most of them would be mixes--most everywhere there are some Germans, often there would be three significant ethnicities.
The Magyars would not like it, they would want a grand Hungarian kingdom (in which Magyars would only be 60 percent or less, but dominating all others). The name of the game is to do an end run around grand nationalities, on paper sacrificing German claims to dominate in the name of a great Imperial union.
As I understand that the way to get that is lots of little bailiwicks in a federation. Is there then any way to
1) get the Germans to drop their own notion of a grand Austria
2) persuade sufficient numbers of local ethnicities to be loyal to this system on the grounds that even if some other group (say Magyars) dominates them numerically as well as through vested power within their county, still their rights as Slovaks or Slovenes or whatever are guaranteed by other blocs of their ethnicity and/or allies at the imperial level
3) distract would-be grand nationalities (mainly Magyars but also perhaps Czechs or Croatians) from the dream of separate nation-states in which they dominate other minorities by suitable local balances of power in the context of the Imperial system
4) persuade a sufficient number of ambitious people of all categories that their opportunities in a large and cosmopolitan Empire are superior to those they might have in several separated nations?
Are such visions completely anachronistic? If the Empire could be reconstituted on these grounds, as essentially one big field in which anyone can aspire to success anywhere within it, it could probably whether the storms of nationalistic separatism of the 20th century pretty well, at least if the thing worked well economically, socially, and politically. Certainly it ought to be stronger militarily come the Great War, if indeed Great Power politics did produce the Central Powers alignment.
It probably would not do to try to call it the Austrian Empire, since that would humiliate at least the Magyars if not just about everyone. Although Napoleon abolished the Holy Roman Empire, could not the Emperors revive the title, on the grounds that it is after all an overwhelmingly Catholic realm? Could it just call itself the Hapsburg Empire perhaps? Danubian is not quite right in view of claims on the Balkan lands, which are pretty important, not to mention Tyrol.
It certainly could not be called Austria-Hungary.
Anyway this is a notion I've long had that is not based on study of the political forces on the ground but on an idealistic top-down solution as much to prevent problems happening generations hence as to deal with the contemporary controversies. Such a solution would not be loved by the Hungarian nationalists--one question would be whether they could accept it at all.
And the biggest question--would anyone in the day have such a vision, and if they did, could they sell it to a sufficient majority to resolve the crisis and keep the Empire together on this basis?