Should I cut into 3?

I’ve been thinking about cutting this into three in hope of propping two and getting the third to branch. Good or bad idea?

If a good idea, where would you cut, and would you remove any leaves?

As an aside, the top is quite heavy and it slumps over a bit. I have it supported with a fishing line tied to my ceiling light. If you look closely at the first photo, you’ll see the line.