Well, there is one of my preferred 1848 PoD (credit to Imperial Vienna for the original idea). Let's assume that the Habsburg ruling circle has an epiphany in 1848 and realizes that the unity of the dynastic state has to be compromised if hegemony in Germany & Italy and control of Hungary are to be preserved. So they decide to divide the Habsburg Empire in four kingdoms.
The Regency Council for Ferdinand I, led by Archduchess Sophie, makes some back room deals with the Frankfurt Parliament which lead to the offer of the German Crown to her eldest son (easily achieved since the early days of the Parliament were dominated by the Habsburg sympathizers). A similar deal is done with Italian nationalists, Habsburg support to Italian unification under a federal constitution similar to the Paulkirsche one in exchange for the Italian crown being given to an Habsburg prince. German and Hungarian nationalists enthusiastically go along with the plan and even Italian liberals are so eager for national unity that are willing to accept an Habsburg on the throne of Italy. A combination of Habsburg prestige (and military power) and grassroots liberal-nationalist revolutionary pressure ensures that all the other German and Italian states accept the plan.
The ancient hereditary Habsburg lands are thus split in 4, Austria (with Bohemia-Moravia and Slovenia) leads the way toward German unification, Hungary (with Croatia) gains the independence that her nobles have long coveted, Venetia-Lombardy (with Trentino and Istria) becomes an effective alternative to a Savoy-unified Italy, and Galicia becomes the rallying point for Polish nationalists.
And what luck, Franz Karl and Sophie had 4 sons, so each can be placed on a throne maintaining the Habsburg hegemony. Franz Joseph becomes Emperor Franz III of Germany (Habsburg stick with continuation of HRE imperial numbering), Ferdinand Maximilian becomes Emperor Ferdinando III of Italy (he revives the Roman imperial title, using the ERE/Byzantine dignities that Ferdinand of Aragon and Isabella of Castile had purchased as a source of legitimacy, and the regal styling Ferdinando III, after Ferdinand of Aragon being I, and Ferdinand I of Austria being II, so that he can affirm precedence over the kings of Sardinia and Naples within the federation), Karl Ludwig takes the Hungarian throne with a Regency Council (which pleases the Hungarian nobles since they could control the Regency Council), and Ludwig Viktor becomes King of Galicia in Krakow again with a Regency Council.
The four Habsburg states immediately form a military alliance and a customs league and monetary union.