The two leagues have not been separate business entities since, I believe, 2000? They both subsumed their business operation under Major League Baseball, so they could not, as you imply, expand or move teams on their own, or make their own rules.
I put together a SABR presentation during which I learned that neither league could move teams without the general consent of their other league anyway until December 1952. They then went to a system that required no no input from the other league. It would be unanimous consent for an NL team to move, and a minimum 6-2 vote for an AL move. The idea of consent from the other league was dropped because they were basically killing off every move the other league wanted to make. That's a key reason there were no franchise moves between 1903 and 1952.