AHC: Western Schism becomes permanent

In OTL, the Avignon Papacy split with Rome based on political factors: The relative influence between the Kingdom of France and Rome itself over Catholic Christendom, and the fact that Urban VI was a tosser.

The split continued even after Urban and the others died. How can this schism be made permanent (or near-permanent) like the Great Schism some 400 years prior?
 
The divided/dueling papacies was abhorrent and a scandal. Which didn't stop the Schism from lasting most of a century, of course.
Still, reunification efforts were attempted for most of the existence of multiple popes. The fact that the source of power for a pope is that he is literally 'Bishop of Rome' severely undermines the authority of any 'papacy' NOT seated in Rome.
One of the more ironic aspects of the 'reunification' efforts was it eventually resulted in THREE popes, increasing the problem, not decreasing it.
I don't believe that having two 'popes' is actually sustainable in the long run,
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So. Have a 'conciliar' compromise 'pope' elected earlier than OTL, before people are QUITE as disgusted with the situation. This means that neither the Rome nor Avignon popes are prepared to resign in his favour, and we have 3 popes.
Now get e.g. the HRE to support the northern Italian one, the French to support the Avignon one, and e.g. Aragon (via the Kingdom of Sicily) to support the Roman one.
https://xkcd.com/927/
Rinse and repeat.

In another century, you have each major Western power blok with their 'own' 'pope', and what are, essentially Autonomous Autocephalous national churches (like the Orthodox have had for a while, or like the Anglican communion has today).
 
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