Fairly easy to do: just keep Justinian's ally and vassal Queen Amalasuntha in power.
A surviving Ostrogothic state means we get a surviving culturally Roman world stretching from the Alps to Egypt, as the Ostrogoths were by far the most Romanised of all the immigrant groups. They'll have occasional spats with the ERE, but the overwhelming strength of the latter will prevent the Ostrogoths inflicting too much damage, whilst persistent Persian problems will hold off any attempted wars of annexation. Anyway, the legal fiction that the Ostrogothic state remained part of the Roman Empire will survive if Amalasuntha does.
This is a scenario that benefits Italy, the Eastern Roman Empire, and Europe in general. I'm planning a TL on it, but how and when it will be published is anyone's guess.