I think the Celtics, first of all, should go for a center. The four I can think of that are reasonable fits Greg Monroe, Andray Blatche, Ed Davis, and Jordan Hill. Of the four, I think the realistic possibility money and stats wise for the Celtics to get is either Jordan Hill or Andray Blatche. Both can score, and protect the rim. Greg Monroe would probably ask for too much money. Ed Davis is another possibility but I doubt he wants to come to Boston. And he may want more money as well.
Then, the Celtics should go for Parsons or Hayward (likely Parsons) for the SG or PF position that needs depth. The way i see that happening is via a sign and trade strategy. And if the celtics are unable to require either of those two, then many can disagree with me here, but I say take Kent Bazemore. He will come for cheap, he has glimpses of Lance Stephenson and he can score. He can give u production of 10-15 points in 20 minutes of a game. I know we are full at the guard position but I think we can get rid of Pressey and take Bazemore instead for better production.