This is a subject I would love to do a TL about one (distant) day, but I fear lack satisfying grasp of period knowledge about to implement (esp. the various dynastic developments). Which manifold PoDs would be necessary to ensure that, starting with a more successful (and longeve) Barbarossa, Henry VI, and Frederick II, the HRE (including the kingdom of Sicily) becomes as centralized and successful as contemporary France and England by the end of 13th century and early 14th century ?
I have thought of some, occuring in combination/succession:
Frederick I Barbarossa kills Henry the Lion in some battle and joins its territories to Staufen demesne, wins a decisive battle against the Italian city-states at Legnano, successfully reconquers Jerusalem and re-establishes latin control in Palestine and Syria in a successful Third Crusade. He gets the Erbreichsplan passed to make the HRE crown hereditary. He lives on to mid-late 1190s.
His son crushes further rebellions of Welf German nobles and Italian city-states, joins southern Italy to the Empire by marriage, changes the HRE homage laws so that minor nobles have to swear loyalty to the Emperor in addition to greater nobles. He supports the Fourth Crusade to put a Hohenstaufen on the throne of Costantinople, revitalized Latin Byzantine Empire reconquers Anatolia, parallel French-English Fifth Crusade conquers Egypt. He lives on to mid-late 1220s or 1230s.
Frederick II gets a different education to care about Germany as much as Italy and reestablish the peace, glory, and prosperity of the Roman Empire, supports consolidation of centralized imperial power in Germany and Italy with legal reforms, although he concedes the nobles, the clergy, and the cities an opportunity to get their voice heard in the Imperial Diet (HRE proto-Parliament). He fights off the Mongols in Poland and Hungary, until Subotay's death stops their expansion in Europe. Economic prosperity in Germany and Italy from domestic peace further strenghtens Imperial power.
Henry VII inherits a stable, unified empire, well on its way to become a centralized binational German-Italian state (with Latin as lingua franca for its ruling classes), makes Poland and Hungary vassals of the Empire, Bohemia-Moravia is fully assimilated into Germany, German and Italian settlers repopulate a Poland, Hungary, and Croatia devastated by the Mongol invasions, turning Pomerania, Silesia, Slovakia, Greater Poland, Kuyavia, and Lodz into German regions, and Slovenia, Istria, Dalmatia, and western Croatia into Italian regions, and parts of the Empire. The HRE sees itself as the natural successor of the Roman Empire, a claim only successfully contested in Europe by the British and Byzantine Empires.
Any other ideas ?
Moreover, what about changes to the rest of Europe fueled by these changes ?
Possible developments I have thought of:
All three crush the theocratic tendencies of the Papal curia, although it is possible that some Pope escapes to France or England and starts an early Western Schism. Eventually the Catholic Church evolves towards a path much like OTL Orthodox Church, with power concentrated in the various self-ruling national episcopal conferences under the tight grip of local monarchs, the Papacy getting gutted down to an ineffective chairman figurehead. The Latin and Greek Churches get reunified.
The Empire, England, Aragon, and major French nobles all vie for influence and fight various wars in France, wrecking the centralization efforts of the French monarchy, although a Plantagenet Empire emerges out of England and western France (Normandy, Anjou, Poitou, Aquitaine), despite some dynastic troubles and internecine strife with barons within England. Resources from France are eventually deployed to accomplish an earlier unification of the British Isles. The Low Countries, Alsace, Lorraine, Franche-Comte, Savoy, and Nice are fully integrated in the HRE, Champagne, Bourgogne, Dauphine, and Provence eventually do as well. Flanders becomes a disputed prize between HRE and England, Paris and central France the unhappy fighting ground as Britain, HRE, Aragon/Iberia, and various French nobles fight war after war there for supremacy in France and western Europe. Languedoc becomes an Aragonese possession.
Emigration from French wars accelerate the Reconquista to completion by the end of the 13th century, Iberia becomes a secondary battleground between Britain and the HRE, although it eventually unifies under Aragon by a mix of wars and dynastic marriages. It takes some part in the contest to control France, even if it mostly focuses towards expanding the Reconquista in northern Africa (Morocco, western Algeria). The HRE gets some chunks of northern Africa as well (eastern Algeria, Tunisia, Tripolitania).
Mongol rampage in the Middle East wrecks Islamic states in Persia and Iraq, as well as Christian states in Syria, Palestine, and Egypt, even if the Byzantine Empire manages to ward the Mongols off Anatolia. The Byzantines manage to reabsorb Syria and Palestine, Egypt turns into a contested area between the Byzantines and the HRE, as do the Balkans.
Persia is conquered and reunified by the Turks, absorbs Mesopotamia, and stalemates the Byzantines.
Antagonism with the HRE economic dominance in the Baltic and a series of dynastic marriages push Danemark, Norway, and Sweden into personal, later real union among themselves and evertually with the British Empire as well.