I'm not clear on what that means.
Let's divide up "private ownership" into 2 types
relevant to socialism vs communism...
Owning the means of production
What would those include? Delineating them is necessary for answering the question.
private property
(eg, homes, cars).
Definitely in favor of keeping that. Humans will never stop desiring to own amenities, comforts, and luxuries. Instead of denying or trying to artificially and forcibly change human nature (which often leads to tyranny), we can instead accommodate it and minimize the negative consequences thereof.