@Roman_Reinss oh I didn't even realize that was taken out. But yes, that should definitely be an option. Can you change the teams when becoming UFA, at least? I'm not that far yet, so I don't know.
And I'll add that the contract negotiations staying the same is a real let down (just read that they haven't changed).
I think you should be able to ask for a sum and term, with maybe your agent suggesting something, but you could make the decision in the end. And the team might offer you something else, and you'd end up negotiating a bit.