On second thought, the sentence in question may have deriven from the following two simple sentences:
The NBA does not only play ball . The NBA does many other things as well.
Therefore, the NBA does not only play ball but also (does) many other things. Eventually, we get "The NBA does more (things) than (it does only) play ball
Probably. We had this discussion on another thread and came to no conclusion. Unfortunately, I could find no reference to this particular 'more than' structure in my big grammar book.