Here I assume that Carroll's four year, $60 million deal is backloaded at standard 4.5 percent increases. That means a starting salary of $14,051,523. It could be set up differently, the most likely alternative being a $15 million flat salary. So note that the Raptors could conceivably have about $950k less available cap than I project here.
DeMarre Carroll $14,051,523
Kyle Lowry $12,000,000
DeMar DeRozan $9,500,000 (not including $600,000 unlikely incentive)
Patrick Patterson $6,268,675
Jonas Valanciunas $4,660,482
Terrence Ross $3,553,917
James Johnson $2,500,000
Lucas (BeBe) Nogueira $1,842,000
Bruno Caboclo $1,524,000
Nando de Colo $1,901,900 (cap hold; $1,828,750 QO)
Delon Wright (20th) $1,257,800
Above roster, if de Colo is let go: $58,208,583
Projected League Levels:
Cap: $67.1 million
Tax: $81.6 million
Apron/Hard Cap: $85.6 million
That leaves $8,891,417 cap room. That's probably too little for a Wesley Matthews (who reports say the Raptors pitched on a starting lineup of JV-Carroll-Matthews-DeRozan-Lowry), and certainly too little for a last ditch attempt at LaMarcus Aldridge.
If the Raptors really needed to, they could move contracts like James Johnson, Terrence Ross, and Patrick Patterson, all of whom could have takers. (Patterson seems like an obvious candidate, going to the Magic, who struck out on Millsap and were interested in his services last summer.) Moving Patterson would free up $5.7 million, enough to give Matthews what he wants. Moving all three would be enough to offer a max to Aldridge.
And remember, the cap may (and rumours suggest it is likely) come in $2 million higher than anticipated. So even moving Patterson and one of Ross/Johnson could prove enough to make an offer on Aldridge, who now has a little more to think about with a top level wing role player in Carroll potentially playing beside him.