Since Brexit supporters can't agree on what type of Brexit they want, I think there should be another referendum. This time have the referendum be a choice between Theresa May's specific Brexit agreement, versus staying in the EU. If the British people vote for Brexit again, it would automatically be Theresa's plan. No need to consult Parliament. Less complexity. Her specific plan ready to implement. If they vote no, Britain stays in the EU.
Another idea is a 3 way vote. Hard Brexit, Theresa May's already negotiated plan, or option 3 stay in the EU. See comments for why I added the hard Brexit option.
This was an interesting show now in podcast.