The Knicks could hold 2.06 max contracts.
The Nets could hold 2.00 max contracts.
The Bulls could hold 1.76 max contracts.
The Heat could hold 1.67 max contracts, even after the team signs its own free agent, Dwyane Wade, to a max contract.
The Clippers could hold 1.02 max contracts.
Link
NYK 2 , NJN 2, CHI 1, MIA 2, LAC 1
So UFA players can get this Max contract by signing with these team.
All the other, if they want Max, need a sign-&-trade.
The question is to know if Joe is in this 8 players list.
It's if they decide to walk away, because they can get Max from their current team, but the interesting part is if Joe really wants to play only for ATL, NYK or CHI, it reduces the list to only 3 Max
If CHI sign 1 Max, and NYK sign 2 Max, then Joe has to sign somewhere else (NJN, MIA, LAC) or it's ATL offer, or it's a sign-&-trade.
And NYK need to renounce Lee if they want the 2 Max... so there is a chance that they don't sign Joe first but wait for a real Max and see who is the best fit after that.
Not the most positive news, but after founding it, I was a little bit more optimist that even if we don't keep him, we have some chance to get something in return, at least more than getting nothing.