What if, contemporarily to the ecumenical council of 870 in Constantinople, Ermengarde of Italy and Constantine of Byzantium formalized their marriage and created a solid bond between the kingdom of Italy and the Eastern Romans? This would pacify the orthodox extremists who claimed Charlemagne and his children to be illegitimate emperors, as the only daughter of the Emperor in the West is marrying the first-born of the Emperor in the East, as well as consolidate Italy as an actual crown and not a mere component of the Holy Roman Empire. It could bring the Pope closer to the other great patriarchs, as now they're all under Byzantium's jurisdiction or at least heavy influence, and it would prevent Italy's disappearance at the hands of Otto the Great a century down the line.