I imagine they would have to run any new show past the copyright holder, but given the long-awaited sequel seems trapped in development hell, I imagine it would be largely a formality. Especially if they get a cut of any merchandise sold.
The problem would be writing an interesting new BJ show. HHN has tried many. many times to come up with a new show. Very few have gained any sort of traction. Theme park shows are an art few are good at, you can't just throw something together. Also, Legal has said no more pop culture parody, which is the most obvious route for a BJ show.