So, this is with a lot of assumptions, but just for arguments sake; we guarantee Iwundu, sign our #16 pick, manage to trade EF/2nd round pick for JR Smith and then waive JR Smith, and waive our rights to all our free agents except Ross/Birch. That would then give us about $23.5M in cap space - so we could then hypothetically offer Brogdon enough to prevent Milwaukee from matching, and still re-sign Ross and Birch.
Player
Cap Figure
Aaron Gordon (24)
$19,863,636
Markelle Fultz (21)
$9,745,200
D.J. Augustin (31)
$7,250,000
Jonathan Isaac (21)
$5,806,440
Mohamed Bamba (21)
$5,697,600
16th Pick @ 120%
$3,117,000
Wesley Iwundu (24)
$1,618,520
Melvin Frazier (23)
$1,416,852
Sub-Total
$54,515,248
2019-20 Dead Cap
C.J. Watson
$333,333
JR Smith
$3,870,000
Timofey Mozgov
$5,573,333
Sub-Total
$9,776,666
2019-20 Cap Holds
Terrence Ross (28)
$15,750,000
Khem Birch (27) - RFA
$1,818,520
Incomplete Roster
$3,588,628
($897,158 x 4)
Sub-Total
$21,157,148
Cap Type
Active Roster Cap
$54,515,248
Dead Money
$9,776,666
Cap Holds
$21,157,148
Total Salaries
$85,449,062
2019 NBA Cap Max
$109,000,000
Actual Cap Max Space
$23,550,938
That would then give us this for a roster:
Brogdon/Augustin/Fultz
Ross/Iwundu
Isaac/Frazier
Gordon/16th pick(?)
Bamba/Birch
You would then probably need to fill roster spots 12-14(15?) with minimum contracts; what you ended up signing Brogdon/Ross/Birch for would obviously figure into that. You might have a $4-5M slot available for spot 12 and just have to fill the rest with minimums.