As Basileios in the old gods start, I managed to convince the supreme patriarch to give me an invasion CB on the Carolingians. I got lucky and captured their emperor early on, but when i ended the war, people from all over my realm broke off, saying I'm not good enough to rule the Carolingian empire. After this, I was given an ultimatum, to continue as Byzantine emperor or Carolingian Emperor. Can I stop these guys from breaking off, continue ruling both the ERE and Carolingian Empire, and get both traits 'Strong Basileus' and 'Crowned by the Pope'?