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.
"Employment" only exists with commodity production. If there is no commodity production, and all labor is socially necessary, i.e. Communism, then no you would not be self employed. You would be an individual worker but bound to the work deemed necessary by planning.
And you could propose work to the councils and planners that you think would be helpful. There’s little reason in that situation, however to go it alone as a “micro-business” or whatever.