10 to 20 percent is a big ask. But still, like all "world religion" questions, this hinges fundamentally on the definition of "religion". Is Ahmadiyya, for example, a distinct "religion" from Islam? In that case, you could have an analogous Mahdi claimant relatively early on just sweep half of Islam off its feet and then wank that sect to the stars. Are the various Hindu sects distinct "religions"? In that case, a relatively small change in Indian history around the time of the Mughals / early colonisation could bring about a novel Hindu sect that manages to gather a majority of Hindus as adherents. Could a semi-egalitarian, stripped-down, proselytising variety of Zoroastrianism have picked up in a post-Sassanid, non-Muslim Persia, and converted the Turkic peoples who were to define so much of medieval Middle Eastern and South Asian history? Sure, but you might as well just call that "Zoroastrianism", right?
If you go by the most stringent definition (a religion as wholly distinct from its influences as Islam), honestly, I think 10-20% is a bit too tall of an order. Islam filled in a very wide gap: a unifying set of uncompromising principles and a community among the Arab people, whose population and social inequality had gradually grown to an unsustainable point. After Islam's rise, there really wasn't a place on Earth where the conditions that give rise to a viable
proselytising religion would exist up all the way until industrialisation, IMO. The Subcontinent is a possible exception, but it seems to have given rise to sects like Sikhism and
Lingayatism that take off on a flying start and then peter out within a particular region. And East Asia, to be honest, is just right out. The Confucian state did not tolerate challenges to its self-preservation as such, so while a bunch of sects more or less distinct from Buddhism and unorganised local tradition have arisen there, none have gathered the momentum to approach state-level power, let alone a significant percentage of the world's population.