Well, there was the Byzantine title Caesar (καῖσαρ) which was subservient to the Emperor, because Caesar was usually awarded to the junior co-emperor or the heir apparent.
It didn't escaped the general devaluation of titles tough. Junior emperors or heir appearants were eventually quickly considered as imperial colleagues rather than Caesar, the title being eventually trampled over by sebastocrat and despot.
Note that Byzantine titulature, tough, isn't only nobiliar but administrative in nature more than it was for Latins until the Late Middle Ages.
If the Byzantines were able to place a ruler on the throne of the Holy Roman Empire
Aaand you lost me.
Seriously, Byzantine emperors barely considered HREmperors as emperors to begin with, they would probably either claim the full imperialship in Italy sooner than to give German's claims much consideration. And that's telling.
True. But maybe if there was a surviving title generally perceived as higher than emperor
Thing is, in the general devaluation of titles, only emperor (and king, altough the boat was rocked on this one in the Early Middle Ages) really escaped the desacralization. And then acknowledging its devaluation, and a fortiori accompaniying its devaluation seems a bold choice for not much reason.
Either you devalue so much the imperial title it becomes meaningless, either you try to do so but fail at it, and you just created a legitimised rival.
Not that you couldn't tweak your way around, trough use of August Emperor, as an equivalent to High King, but I wouldn't see a brand new overlording title just popping around.
Augustine could work as a title.
Like Charles The Great, Augustine of Christendom
IOTL, Carolingians and Ottonians emperors used the title of "August Emperor" which more or less carried this idea of overlordship over Christiendom.