Orinsul: A constitutional papacy, eh?
Why not?
With the states states the papacy is two things, a temporal secular power and the Church.
I can see that if the Papal States expanded their borders, as any player setting out to conquer the world with them would do. They would need to either expand the ecclesiastical government to cope with the new territories which would be very difficult and a big change for the conquered people creating instability and the like.
Or expand secular government.
Now if the Papal States came to constitute the whole of Italy it would be hard pressed to manage.
The simplest and most likely solution would be to adopt a model not unlike that of a constitutional monarchy.
Where the Secular government, the day-to-day running of the Country, would be delegated to the hands of an elected parliament.
With the Bishop of Rome, Servus Servorum Dei, remaining the executive, Head of State, but the secular government being handled by a Head of Government and cabinet under him
Caesar onto Caesar.
its the only way i can see that a Papal State that either survives into the 20th century or outgrows its established borders would be able to avoid revolution and abolition. And from the sort of views held by the people who were become popes near the end there its the most likely too.