Anyone but the Habsburgs

The Wittelsbachs and Luxembourgs are the best candidates for alt-Habsburgs, as far as Imperial families are concerned. At one point the Wittelsbachs held the Imperial throne (well, technically twice, but Charles VII was a compromise candidate during the War of the Austrian Succession),

Technically we have the following Wittelsbachs at the head of Germany:

*Louis IV the Bavarian, Holy Roman Emperor (1282-1347). King of Germany (reigned 1314-1347), Holy Roman Emperor (reigned 1328-1347). Died during a conflict with his rival Charles IV (of the House of Luxembourg) who had been set up as a rival King of Germany. Charles IV was victor by default and stayed on the throne from 1346 to 1378.

*Rupert, King of Germany (1352-1410). Elector Palatine (reigned 1398-1410), King of Germany (reigned 1400-1410). Actually "rules" a Holy Roman Empire which is in disorder and suffers from economic problems. But he had managed to create marital alliances between his children and the rulers of Sponheim, Lorraine, England, Cleves, Austria, Pomerania. His political situation seems to have been improving but his sudden death ended his plans. His death was followed by a civil war for the German throne between two rival candidates from the House of Luxembour (first cousins to each other).

*Charles VII, Holy Roman Emperor (1697-1745). Prince-elector of Bavaria (1726-1745), Holy Roman Emperor (1742-1745). A powerless emperor who did not even control his own personal domain. His reign takes place during a war against the Habsburgs and his opponents occupied Bavaria for most of his reign. He actually managed to recapture Munich three months prior to his death. His sudden death allowed the head of the House of Lorraine (married to the currentn head of the House of Habsburg) to gain the Ccrown of the Holy Roman Empire.

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The best chance for the Wittelsbach to stay influential is if Louis IV lives for a few more years and manages to defeat Charles IV. Which seemed likely at the time of his death.

Charles was set up as King by a hostile Pope and was initially seen as a mere puppet, even mocked as a "priest's king" (Pfaffenkönig). Many bishops and imperial cities simply refused to support the rival king, Papal wishes be damned.

It didn't help that Charles was in a rather weak position in 1346. He succeeded to the throne of Bohemia and Luxembourg when his father was killed at the Battle of Crécy (26 August, 1346), fighting with his French allies against the English. Much of his army him died with him and Charles had to rebuilt the military forces of their House.
 
Maybe the Jagiellons, should they not die out? Or the Vasas, IOTL branches ruled both Poland and Sweden. Granted, those branches regularly warred between each other...

Not without a reason. Sigismund III Vasa (1566-1632) was elected King of Poland in 1587 and managed to defend his throne in a brief war with a rival candidate, a Habsburg. He was at the time heir apparent to the Swedish throne.

In 1592, Sigismund's father died of natural causes. Sigismund succeeded to the throne, creating a Crown Union between Poland (Catholic) and Sweden (Lutheran). He chose to remain in Poland and set up a paternal uncle as a de facto regent in Sweden. So far, so good. Sigismund was himself Catholic but at least attempted to respect the religious rights of his Swedish subjects. The crown union lasted from 1592 to 1599 with little apparent incident.

Unfortunately, Sigismund's role as a champion of Catholic Counter-Reformation in Europe led to concerns that he would inevitably try to bring Sweden under the rule of the Pope. His uncle Charles (IX) (1550-1611) was not particularly loyal and spread rumors to that effect for years. The Lutherans needed a champion and Charles "selflessly" volunteered. In 1599, Charles deposed his nephew in a coup. Serving as an official regent for a few years, then declaring himself King of Sweden in 1604.

Naturally, Sigismund did not peacefully accept his deposition and a prolonged conflict for the Swedish throne started in 1600. If Sigismund realised the threat unce Charles represented earlier than 1599, we might have a different conclusion to the crown union.
 
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