It seems to me that it was possible to buy shares in MLB teams at one time---maybe 20-30 years ago. Baltimore comes to mind for some reason but I could be wrong.
In the early '70's I purchased stock in the Clevland Cavs. Owned the stock for about five years and then they went private. Got about $1.00/share (I had paid $5.00/ share) plus two tickets to a game in the cheap seats.