You can do that right now in every modern socialist country, but what about the USSR and the Warsaw Pact? And any future socialist and communist experiment(s)?
By self-employment, I'm indeed referring to running your own business, but I'm referring to a sole proprietorship or freelancing, not your typical business where other workers are exploited for the benefit of the owner.
It's also a worker's co-op of 1, lol.
Socialism has many definitions. Some formulations could end up with sole proprietorships. Anything that's basically artisinal and can be done by one person has the potential to be like this. Different socialist societies can decide this kind of thing on their own.
Under communism, class separations would be minimized, even cease to exist, as the working class abolishes the other classes (and then itself). It's an interesting question of whether this means a situation in which you'd become a little bougie (sole proprietorship) would be impossible, by law and social convention, or whether the conditions would make it impossible for this to be bougie and you can do whatever you want in terms of making and selling stuff because it will never actually be able to acquire a bourgeois character due to systemic effects (like post-scarcity).