As
@EternalDawn said, it'd be hard to retain the Empire united. Although, the Romans DID in fact maintain a united Empire at times. There are notably different political systems, cultural influences, etc.
However Otto III also did a number of peculiar things that suggest that he might well succeed - he was trying to re-establish the Roman Senate, he worked with the Pope on religious reform - and maintained power over Germany whilst ruling from Rome (however short that was).
Genuinely, I think the key to a survival relies on first the establishment of the Senate in Rome, which I expect would have to include all the significant Lords of the HRE - and through that formalise the appointment of regional rulers (perhaps even going so far as to have heavily weighted elections of the "Princeps Germanicum").
Second, if we assume a successful succession (that could go messily, but I imagine Zoe could hold it together) for the heir (Lets go with baby John/Ioannes) could have a shot with the unification of the German, Italian and Roman nobility into a single massive Roman Senate. I think the major concern is that the Empire might well fall into a 3-way Shogunate of sorts, with the German, Italian-Balkan (especially if Hungary was invaded), and Greco-Anatolian regions all effectively having powerful regional leaders.
At the same time, that potentially extreme decentralisation could also have benefits. Germans aren't likely to be ruled by Romans, Romans aren't likely to be ruled by Germans, making the Emperor less powerful, but also less 'obnoxious'. Do I think that'd happen by design? NOOOOOOOO. It'd be entirely political compromise between Otto III trying to ensure control over Germany and Zoe trying to ensure control over the Romans, with an army in Italy to ensure the middle.
Whilst you'd be hard pressed to convince people that Zoe was indeed "Macedonian" a merger of the Ottonians and Macedonians is one hell of a prestigious dynasty to be part of.
Going further, I think one key that would help would be 'John' calling for a Crusade - "Where those who serve may rule their land either as Roman or German" (as in style of rule). On one hand, yay - the Romans would probably like having more security out east, and the Germans would certainly appreciate the opportunity to get rich.
This would lead to a weird patchwork of Roman and German-Feudal rule in the Levant (I reckon together the Romans and Germans could probably take on the Fatamids and win) this actually is a "Good Thing" - the two systems intertwined can learn from each other and improve, and the Romans and Germans in the region have exposure to help reduce animosity since they fought together, rule together, and have to ensure that they aren't trashed by whoever wants to retake Egypt.
So would it be a true Empire - yes. Deeply oligarchical and a weird hybrid, yes. Very powerful, certainly. Prone to fall apart? Certainly. But as long as the Emperors can continue to convince the Germans and Romans to work together to make the Med their looting/stomping ground then I think the wealth they can get (and the 'bleeding' it gives the body of the Empire) helps bring some level of stability.
Whether it could genuinely reform, or solve its religious problems however - THAT is the biggest powderkeg IMO.