Indo-Persian Empires

Apart from possibly the Mauryan, Macedonian and Mongol Empires, which non-Muslim power was capable of ruling / conquering much of Persia and India?

Not sure about plausible it is though at maximum am looking for a scenario where an Indo-Persian Empire is formed, whose territory is composed of much of the Indian subcontinent up to the East bank of the Tigris River.
 
Apart from possibly the Mauryan, Macedonian and Mongol Empires

Mongol Empire? The Mongols were repulsed every time they tried to invade the Delhi Sultanate, and the Delhi Sultanate only came to an end with the Mughal Empire, ruled by the Timurid dynasty. Though, all things said, a Mongol India is certainly possible, though I doubt a successor Mongol state would control both India and Persia.

Not sure about plausible it is though at maximum am looking for a scenario where an Indo-Persian Empire is formed, whose territory is composed of much of the Indian subcontinent up to the East bank of the Tigris River.

The Ghurid Empire fulfils your scenario quite nicely.

1024px-Ghurids1200.png


Their collapse led to the rise of the Delhi Sultanate, which was the nation that really situated Islam in the Indian subcontinent. They were drastically more Persian than (pre-Islamic) Indian - but then again, even the Hindus in the court of the Mughals spoke Persians and knew of Persian myths. To avoid the collapse of the Ghurid state, it would probably be in order to avoid the Khwarezmid invasion and/or butterfly away the power struggle after the death of Muhammad of Ghor.
 
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