PP+SVI for Caruso doesn't work. The Celtics would need to add 2 more players to get to the number, because PP is poison pilled (he counts lower as dollar value in the trade for the Celtics than he does for the Bulls.)
And if PP isn't in the deal, now you need to trade 5 guys -- the entire roster, excluding two ways, outside of your top 9 (6 + PP, Hauser, Kornet), and then sign bodies off the street/convert 2 ways to get to the roster minimum. And that doesn't even get into the difficulty that would put the Bulls in roster wise.
The only realistic way the Celtics add anyone is with the TPE**. There are options, but most won't move the needle absent including significant draft capital.
For example, if you want a big, Nick Richards fits into the TPE, but I imagine will cost a lot for a guy that might not play often.
Would the Wizards trade Kispert?
**The Celtics can't trade for a player with the TPE, then include that player in a 2 for 1 for another player before the deadline. After a player is traded, you have to wait 60 days before that player can be included in an aggregation in another trade, though that player can be traded again straight up for another player (unless there's an additional restriction on players acquired with a TPE than I am unaware of.)
Edited to fix inaccuracies about the cap.
