Okay, in the early 17th century (1610s-1630s) a large amount of the Khoshut-Oirat Mongols migrated west after a conflict with both the Khalka (eastern) and other Oirat Mongols. They became known as the Kalmyks, and settled in the area known today as Kalmykia (although their initial settlement area was much larger). They were Tibetan Buddhists, and several hundred thousand of them migrated (definitely more than 200k).
However, what if a much greater amount of them migrated from Mongolia and joined the movement west. I'm thinking many more of the Khoshut-Oirats, around six or seven hundred thousand of them. In OTL, they expelled the Nogais and Tatars from the land they settled. With three times as many Kalmyks incoming, how much more could they have conquered?
If it makes a difference, let's take Russia out of the equation... say it remains divided, and the various Tatar khanates stay ruling there. How much could they have conquered? The Crimea? the Don-Volga valley? What about the Kazakh lands, who the Kalmyks invaded on their migration. How plausible might that be?