As it says on the tin.
There are some old threads on the subject, but none of them really address the basic question here. What exactly would the Hohenstaufen Emperors have to do to address the problems with imposing imperial authority?
Henry VI succeeds at making the crown hereditary and say he lives another twenty years or so (give or take) and say Frederick II is raised to think of himself as an Emperor first and king of Sicily second. Let's throw in having the succession secured by at least average-competence emperors into the 1300s. The kind of stuff any sufficiently imaginative writer can dream up.
Fine. All of this is easy from the Alt-historian's perspective. Seen it in a dozen threads and half as many timelines.
But what do they have to do beyond that? Does Imperial law need to be changed to give the position more power? Or is it more like France, where the Hohenstaufens have to build up a power base through control of land and ideally the new cities to be able to crush any would be quarrelsome subjects so as to turn de jure authority into de facto? Something else?
And where are the resources (of men, of money, diplomatic trumps to play in that game...all of them) coming from? Where can the Emperor turn without having his attempts to secure support in one region causing him to have to make compromises that will see his authority unravel in the second region?
No point in controlling Italy at the expense of any authority in Germany, and not much more the other way around.
But not very many nobles or city-states - even if not actively opposed to the Emperor - are going to eagerly lend support in Imperial projects designed to strengthen the ability of the Emperor to use them for his plans and his ambitions but at their expense.
One good thing the Hohenstaufens have is that if the position is made hereditary, then the ability for a would be anti-king to do anything is...extremely limited. The Pope's role in the process has been rendered about as relevant at the archbishop of Canterbury.
It might take some work to make that work alongside establishing a functional relationship with the Papacy, but I presume support for things like crusades would make it hard for the Pope to openly oppose the Emperor without it seeming to be purely a matter of spite, and after the initial disturbance it would sooner or latter reach being the status quo on its own.
All things otherwise being favorable, at least.
Note: I'm using "centralization" to mean "power to the Emperor" - the HRE being a truly centralized state in any sort of modern sense will take a long time, but the Angevins OTL seems to have been fairly successful despite the Magna Carta and the Capets managed to make it over the obstacles in the period (late 12th to early 14th century) in question. Being more successful than either of these would be nice, being as successful as the Capets were at establishing royal authority on firm foundations that could and did endure and grow still further as time permitted is the task that - somehow - the Hohenstaufens fell short of.
And judging by the threads involving "centralized Holy Roman Empire" or "successful Holy Roman Empire", it appears to be a community consensus that the possibility is worth discussing - but as none of those provide much detail on the "so how do the Emperors actually get the resources for the changes necessary?", I'm starting this one.