Well, that's certainly an...unexpected question. If Russia spent a lot more resources on infrastructure in the Far East and Siberia, and was a lot more aggressive in the Far East (at the cost of much of Central Asia and a lot of Eastern Europe), I could see Russia controlling Xinjiang, Manchuria, all of Mongolia (including Inner Mongolia), possibly Korea, and maybe Beijing. But Beijing is pretty improbable.
EDIT: Actually, this is kinda interesting. For a specific POD, I'd look into somehow turning Peter the Great's point of view away from the west and more towards the development of Russia as a unique, independent, powerful, industrialized Eastern power. Maybe a Chinese tutor at court? Then you could see some expansion to the east during his reign and likely even more under the Romanovs post-Peter.