The use of the word "Soviet" already implies Russian domination. Russian was not a prestige language nor the preferred language of communists. The terminology of Marxism is in French and German. If the communist revolution starts or is largely directed from Russia, then it's demographically impossible for Russians not to dominate. The areas that an ATL Soviet Union could conceivably consolidate given the best circumstances are largely areas that already had a history of heavy-handed Russian imperialism.
The OP asks:
"The question here is whether we can devise a Soviet Union that is inherently a multinational state by virtue of its inhabitants and more-than-Russian by virtue of its borders. In simpler terms, include from near the outset a large population and territory that were never within Imperial Russia."
To rephrase what I said before, an inherently multinational communist state would not call itself the Soviet Union. If it calls itself the Soviet Union, it means that they roughly control the area of the former Russian Empire. If a communist state incorporated, say both Germany and Russia on an equal basis, they would call themselves the People's Revolutionary State or the International Socialist Union or some such.
It's like asking for a Scandinavian union called the "Danish Confederacy" in which Denmark is not dominant. It's physically possible for that to happen, but it would require a statesman proposing a nonsensical and politically inflammatory name for his country, and for Swedes and Norwegians who have as much say as the Danish to be just fine with that. It doesn't make sense. "Russian" may not literally be in the name of the USSR, but Soviet is a specifically Russian word not used by Marx or Engels. If a federation of the USA, Canada and Mexico came into existence 400 years from now, and it was called "EUNA" by foreign countries after "Estados Unidos de Norteamérica", then clearly Mexico is the dominant partner and Spanish is the lingua franca. Why would an English speaker not call it "USNA" (United States of North America) if Mexico and the Spanish language didn't take some kind of precedence?
What you might conceivably have, is a Marxist state that calls itself "The Union of Socialist Workers' Councils" in English (just as an example, it doesn't have to be exactly that), with the constituent states translating the name into their own languages. The Russians might say "Soviet" in their language to mean council. Of course, this ignores the fact that a socialist state of that size is basically impossible. I don't see both Germany and Russia having revolutions, and even if they do, I don't see them forming a unitary state without significant problems that will lead to inevitable disintegration or chaos.