I think a GM can handle this to some degree by saying, ‘hate to lose you, but we’ll look to find a situation that works for both sides. If you want to leave I need 8 teams you’ll approve a trade to. If I get acceptable offers outside the list, I’ll bring them to you as well, as the top 8 may take longer’.
The eight teams will likely be Vegas, Dallas, Tampa, Colorado, Florida, and three rotating options, so those top 5 will still get first crack at a number of players, but Montreal, Philly, NYR, Chicago, Boston, and maybe SJ, Utah, and Anaheim will be on lists.