The basic unit of economic organization is the Corporation. This is a non-person eintity that can own goods, make agreements, and the like.
Historically, creating such a corporation required government assent.
Smaller organizations, like partnerships, are sort of like them as well.
Modern "Western" economies have a mixture of privately owned corporations, publicly owned corporations, state corporations, nations, non-profit corportations (which are not owned) of various kinds, etc.
I could interpret your meaning as stating the privately owned and publicly owned corporations don't exist.
Examples of such an organizations engaging in commercial purposes is Ikea, most national postal services, central and regional banks.
Now, in the past half-century, there was a massive economic war between "Capitalist" and "Communist" states, and the "Capitalist" states won. Nations that did not ally with the "Capitalist" states where economically isolated, invaded, attacked, overthrown and destroyed by the winners of this war.
Despite this, some "Socialist" economies have persisted and flourished better than similar nearby "Capitalist" economies. An example is Cuba, which is richer than the nearby island of Haiti and Dominican Republic (both halves!) despite being both invaded and under economic sanctions from the nearby super power economy (USA).
Corporations themselves almost universally operate as "Socialist" organizations within themselves -- Command Economies. And there are Corporations whose size exceeds that of many nations.
That isn't to say there aren't horrible traps that Socialist centrally planned economies fall into.
Corporations avoid them through a number of ways. They aren't the primary power, so their rulers must obey the rules of the state in which they are embedded. This prevents them from going off-the-rails in power-centralization and protection (the dictator trap, where you turn state power into an engine of protecting the current set of rulers).
As they are relatively small, they often have competition. Their ability to use their power to crush their competition is limited by the state they are embedded in; which means even strong corporations can eventually be outmaneuvered and fail if they stop generating excess value efficiently.
Newly large capitalist corporations almost always have recently successfully generated a whole pile of surplus value in order to grow. Inertia keeps them doing what they have been doing, with minor corrections (their correction process was also possibly successful at smaller scales).
Over time they'll drift. If they remain long, they almost always have a natural monopoly they have managed to corner. They now drift, protected against competition to some extent by their monopoly power. Sometimes they drift into being really inefficient; that is when competition can grow and threaten them. Sometimes they drift into being more efficient.
Cross-transfer of corporate culture occurs, where what other successful corporations are doing is imported via business school graduates, hiring workers from their businesses, etc. This is another source of culture drift, almost unavoidable if a business wants to grow at a fast pace.
And then they die. They are torn apart into their assets, and new Corporations claim their "territory".
States could do much the same thing, but traditionaly States "death" involves violent war, revolution, and a lot more destruction than Corporate "death".
So one approach would be to invent an authority that prevents overly violent "death" of States, and prevents them from going into the trap of protecting the ruler's interests against the interest of the State or the (entire) People.
Another would be to point out that the advantages Corporations have over States is mostly long term. In the short term, it is perfectly plausible for a medium-large "Socialist" state to function. The Soviet Union went from an agricultural economy to one capable of defeating the German Empire and then holding off the most powerful industrialized nation for a half-century in a few decades under a centrally planned economy.
Another approach is to solve the problem with information. The theoretical advantage markets have over planning is that markets solve pricing problems better. A genius economist with modern computers might be plausibly able to solve the pricing problem without markets.
Doing so accidentally would easily be reasonable, and sustaining it for a while as well.
The biggest problems against such an experiment in our world is both the extreme risk that it would fail (and cause untold suffering), the violent reaction of the capitalist western economies to such an experiemnt, and the fact that this doesn't prevent the "protect the king" dictatorship trap.