And while Śaṅkara was perhaps nondualism's purest and most famous exponent, it was taken up by many others in various ways – including by very different enemies of Śaṅkara. The later theistic thinker Rāmānuja wanted to assert against Śaṅkara that the plurality of things in the world is real, and yet he accepted Śaṅkara's basic nondualism: his philosophical system was called Viśiṣṭādvaita, differentiated or qualified nondualism. He aimed to produce a harmonious synthesis: the plurality of the world is not an illusion, as Śaṅkara would have it, but the parts of the divine One.
Now while Rāmānuja could be harshly critical of Śaṅkara himself, he remained in Śaṅkara's basic camp of loyalty to the Vedas and especially the Upaniṣads. Śaṅkara had much greater hostility to the Buddhists, who rejected the entirety of the Vedas and Upaniṣads. And yet – here is the striking thing – a very large number of Buddhists themselves accepted nondualism. The Yogācāra school had been taking up some form of nondualism since before Śaṅkara's time, enough that to other Vedāntic thinkers Śaṅkara's school just looked like the Buddhism they were familiar with; for that reason they even called him a "crypto-Buddhist" (pracchanna bauddha).
But it is crucial that most of the thinkers I've named here do not cite experience as the ground of their claims. Wilhelm Halbfass in India and Europe reminds us that Śaṅkara never refers to any experiences of his own; Chinese nondualists like Zhiyi didn't either, according to John McRae and Robert Sharf. But if anything, I think that nondualism's non-experiential provenance gives it more plausibility. That is, nondualism's exponents did not merely see it in an altered state of consciousness, but viewed it as somehow a logical necessity.