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Your challenge is to make Catholics (those who at least nominally owe spiritual allegiance to the Roman Pontiff) more than 50% of the world population.
Must haves:
Catholic Church must still be a hierarchical organization with a clearly defined central leadership
The leader must still claim to be the Vicar of Christ and successor to St. Peter
The central leadership must be sovereign in its own right (owing no allegiance to any temporal power)
Ideals:
Church HQ still in Rome
One or more native empires in the Americas survive and become Catholic monarchies in their own right
The Asian giants China, India, and Japan largely remain with their pre-existing traditions, so the easy way of converting these countries is closed.
Challenges:
Eastern Orthodox reunite with Rome
More native African kingdoms like Kongo are recognized as Catholic monarchies on an equal basis with European ones
Protestant Reformation either averted through internal reforms, or total Catholic victory during religious wars, or Protestants becoming a marginal sect