Those in charge didn't need to own a lot; they controlled it, and had private stores, special living arrangements, their own hospitals. For which they paid the same as peons did in generally available stores, apartment blocks, and hospitals.
Except one would have lard and poor quality sausage, the other would have pork loin; one would have good heating and 10 or 15 sq meters per person, the other would have 2-3 square meters per person; one would have aspirin and people would be kept in wards with a dozen other sick people, the other would have Western antibiotics and private rooms. Who needs capitalism when the socialist parties top dogs live like oligarchs and their not top but still highly ranking folk like the bourgeoisie? It worked the same for education, vacations, everything. In a classless society, class was based on loyalty to the ideologie du jour and the powers that were.
A lot of Western companies did well trading with the owners of the USSR. Not as many as did later, because terms and conditions were subject to a lot of caprice, and the USSR didn't pay well for a lot of things. The ruble wasn't convertible, you couldn't actually own any of the production facilities, and hard currency was always in short supply. Still, in the '70s a number of wealthy Westerners did okay. For example ...
The Zhiguli was a staple Soviet car. Small, cheap. It came about in the 1960s and was produced in a town built around the new car plant, Tolyatti. Tolyatti was named after Togliatti, and Italian communist. It was named after him because the car plant was built and the car produced in cooperation with Fiat. The Zhiguli, "Lada" in the West, was a modified Fiat. This kind of public-private partnership was much more common outside of the US, which had an ideological aversion lacking on the part of many European countries to collaborating with a country with millions in GULags, a strictly authoritarian cast to its politics, an a history of repression. Then again, this typically happened in countries that shared a certain official ideology with the USSR and were willing to make excuses for repression that they found less oppressive, while the USSR and esp. the US were adversaries, and the USSR had the overt goal of destroying NATO and bringing about the downfall of the US.
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