We have a lot of second round picks that I'd trade to get some upgrades on expirings. For example, I'd trade a second and James Young for Omri Casspi, who wants out of Sacramento. And I'd trade Zeller and a second for Bogut, assuming Bogut is healthy at the time of the trade. I don't think those moves would hurt chemistry at all.
I'd also make a big move for someone like Cousins, obviously. Rozier and Mickey work salarywise for Noel, and I don't think that'd hurt chemistry on the outgoing player side, but I'm not sure how good of a teammate Noel is. If the Celtics thought he'd be fine, I'd add the Memphis first to my above package, but at the present time, I will not be upset if Noel isn't here.
I would only trade Amir for a star. I know he can't rebound much these days, but he makes all the right plays on offense and defense.