there are a few opportunities for this, IMO, both of which take place during the yeltsin years.
during his first term as president, yeltsin was trying to change the constitution, but was opposed by the supreme soviet and the congress of people's deputies. yeltsin declared the congress disbanded by decree, but they refused to accept this and instead declared that yeltsin was removed from office. for a while this was the status quo, with both of them acting independently. there were street protests against yeltsin and his privatization/neoliberal economic plans, and there were clashes with police which in some cases became running street battles. the army ended up siding with yeltsin, however. they shelled the parliament, killed a bunch of people, and secured yeltsin's power.
however, we can posit a situation in which the armed forces go the other way, siding with parliament over yeltsin. while this does not on its own lead directly to a communist russia, it certainly derails and likely rolls back the neoliberal changes which were already starting to play havoc with the standard of living in russia. it also leaves in existence structures of soviet government, which are manned by people who are not exactly friends of capitalism. so that's one way.
the other way I could see is if the 96 elections go to zyuganov and the communists rather than reelection for yeltsin. how this could be accomplished: somehow negating the effect of western interference in the election or the fraud perpetuated by the yeltsin camp, or securing such a huge majority for zyuganov that it is impossible to ignore. in my opinion, the former is more doable here. zyuganov had a solid amount of supporters, but nothing like the landside necessary for the latter option. so if the 96 elections are completely free of interference and fraud, you could see a communist president. I think there was a brief TL here on that subject a while back, but I don't think it really got off the ground.