IMHO a possibility might be a Berengar I more successful in handling the Hungar problem. It would give him the chance to consolidate a hold on the great feudataries and, together with a successful expulsion of Saracens from the Gargano peninsula in Puglia (which he carried out successfully IOTL) would put him in a very strong position with the church. For what is worth, he even managed to be crowned emperor but his power base was not strong enough due to the Hungar incursions and his demesnes were in Friuli, not right in the middle of the Padan plain.
Even assuming that he manages the Hungars and appoints as heir his grandchild Berengar II (Berengar I had no sons, just two daughters. One married the marquis of Ivrea, Berengar II is her son) there are still a number of issues to manage: let's say that East Frankia is still unsettled, and his north border is relatively secure (and possibly the Hungars repelled from Italy might put pressure on them), but he still has to deal decisively with the duchy of Spoleto (another family with regal/imperial ambitions) and with the kingdom of Arles (which IOTL intervened in Italy, although with much success). And of course the papacy in Rome has to be handled with a lot of care (Spoleto is close enough to Rome, and the dukes had always a faction in Rome, often the strongest one). A possible winning strategy might be to try and conquer the south of Italy, starting with the semi-independent lordships and principalities in Campania. Sooner or later he will have to deal with the remaining Byzantine territories in the south of Italy (Puglia, Calabria and Syracuse IIRC): a window of opportunity might come with the assassination of Leo V in 820 and the rebellion of Thomas the Slav. Taking advantage of the weakness of the ERE (and the surge of Arab attacks in the east) a show of force coupled with a judicious amount of bribes might be enough.
I will stop here, since I do feel this is becoming a Berengarian wank.
My idea is that Berengar has a window of 20 years (820-840) to gobble up southern Italy, put Rome firmly under his control and take advantage of the troubles in the kingdom of Arles. If he manages to do that (and it is a big if) then there is an HRE based on Italy.