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The goal: turn the Russian Empire into an unpleasant memory. Sever the 'stans & either make them independent or turn them over to the Ottoman Empire (preferably, it survives). Karelia becomes Finnish. Ukraine, Byelorus, & other European territories either become independent or are taken by Polish Commonwealth or the OE. Siberia becomes independent (united with Mongoila? partly taken by China?), except for the Pacific Provinces, Sakhalin, & Kamchatka, which are taken by Japan. A rump Muscovy survives.
POD any time between 1840 & 1900.
Edit: I pictured this being connected to a 19th Century war, but I wouldn't be averse to anything back to about 1700, not least because a number of posts have suggested it's too hard this way...