Portugal manages to conquer significant parts of Andalusia during the Reconquista, politically manoeuvring around Castille, Leon and Aragon.
After extending the Reconquista to N.Africa much earlier than OTL (i.e. Tangiers, Fez, Marrakech) Portugal sees itself as the Western Bulwark of Christianity in much the same way as the ERE did.
Eventually navigates politics and war to unite all the Christian Kingdoms of Iberia into Portugal.
Mongol invasions go incredibly well - whilst deflected by the ERE, the Mongols charge across Europe, forming a new Khanate that stretches to the Pyrenees, where the Portugese defend against the Mongols with reinforcements from their N.African Territories.
The European Khanate for some reasons declares itself Muslim, beginning the emergence of a common Catholic identity for the Europeans who don't convert and stay the majority.
The Khanate throws the Pope out of Rome, who seeks refuge in Portugal, eventually becoming a Patriarch of Santiago (Or whateva).
After a significant succession crisis the European Khanate collapses into dozens of smaller Khanates - Creating an opportunity for the ERE and Portugese to seize territory.
In a treaty between the Portugese and Romans, Europe is split along the Alpine/Danube/Libyan borders with Portugal being accepted as WRE. This coincides with a union between the Catholic and Orthodox clergy that accepts that the filoque is not enough to cause division - after all, Muslims and Mongols.
Romans take OTL Hungary and Italy, whilst supporting Portugal in their reconquest of the Frankish Khanate, and later the German Khanate.
Whilst the ERE focuses on reconquering Egypt, and expanding into Mesopotamia, the Portugese WRE Expands into the Polish Khanate, later extending their rule throughout the Baltics and OTL British Isles.
Acknowledging the difficulties in ruling the territories, the WRE and ERE jointly found the North Roman Empire (NRE) - a state in the Modern Russias, with the WRE sacrificing the Baltics, and the ERE Sacrificing control over Taurica.
Dominated by a Greco-Roman-Portugese nobility that identifies as Christians, it is supported to settle and dominate OTL Russias upto the Urals.
The NRE expands over the Urals when the WRE conquers the New World, and the ERE happily dominates South Africa, East Africa, and the East Indian Trade.
Yes - it is utterly bonkers, and details galore are being ignored - but that is about as close as I think you'll get to your aim. It'll be partially Portugese, which in this world would be even more "Bring the Lord to the Heathen, Crusade, Rah-Rah-Rah"
The PoDs would need to explain
1) How Portugal dominated S.Iberia successfully.
2) How the Mongols Kicked European ass to the Atlantic
3) Why it was a Muslim Khanate
4) How the Schism was resolved alongside the reformation of a 'Christian Roman Federation' of sorts
5) Why the WRE went west (Economic war with the ERE? Discovery of EPIC FISHING in the Grand Banks? Lucky Discovery exploring West Africa?)