This may not be what you're looking for, buut-
You might keep a USSR by simply having Yeltsin or an alt-Russian president be interested in keeping a union together. In OTL, Yeltsin thought Russia could do better, and he could do better personally, by ditching the other republics.
If the Russian leadership wants to keep a union, the Baltic states, and probably Georgia will still go, (not to mention the Warsaw Pact states), but the Central Asian states, which had independence thrust upon them, would gladly stay in the union, as would Belarus and even Ukraine (though with more west Ukrainians interested in changing that status).