If they bring back virtually the same team, including re-signing Fournier for what he's likely to command, then that means the owners are willing to pay $50+ million in luxury tax for a team that will probably be coming off a first round loss.
I believe the owners would be willing to pay a large luxury tax bill (not sure about how large) for a team with a chance to win a title. Can you really say that a team coming off a first (maybe second) round exit is ready to make a title run? Yes there are excuses for this season, but even with those excuses considered I think it's a stretch to see this group as a contender.
My belief is that the team is going to be forced to look at their options for moving off salary. That could mean Kemba, or it could mean Smart (who will be in the last year of his deal) and Tristan Thompson.
I like Kemba, and he's looked a lot better when he's been able to rest. I also think that the ceiling for this team is much lower without the healthy, productive version of Kemba we have seen at times this year. Nonetheless, I think the best case for the off-season is probably that they trade Kemba to a team with cap space without having to give up assets to move his money or take back any big salaries. Then they would be in a stronger position with respect to looking at trade options for Thompson.
Worst case scenario is that they can't trade Kemba without giving up 1st round picks or taking back big salaries. This could then force them to let Fournier walk for nothing, or else use Smart or other assets to move Thompson.
I think there's a good chance the Celtics head into next season with mostly the same team, minus one or two of the players who are currently key parts of the rotation, and despite that loss are still very close to the luxury tax line and have little flexibility to add talent.
In this context, the fact that neither Nesmith nor Langford has really shown much so far really hurts. The Celtics can't head into next season realistically expecting to rely on either of those guys to be contributing parts of the rotation -- not if the Celts want to be more competitive next year than they were this season. Similarly, the Celts can't really hope to use either of those players as significant trade assets.
So to answer your question --- how will the Celtics improve this off-season -- I'm really not sure.
I think coming back with Tatum, Brown, Rob Williams, Pritchard, and Fournier all healthy will make a difference.
Beyond that, I think the focus would be on finding ways to exchange the younger cheap players on the back end of the roster (e.g. Carsen, Grant, Nesmith, Langford, etc) for more experienced cheap players (similar to what they did bringing in Theis and Wanamaker a couple years ago).
Parker seems like a decent reclamation project and he might be a fit here next season. Luke Kornet has impressed me as a defender and seems like he has upside as a 10-15 minute rotation staple who gives you big man defense and spreads the floor a bit. Danny needs to find more guys like that who can play and have at least a couple of NBA level skills yet cost $2 million or less.
Getting the main guys healthy, having a consistent top group of 5-7 players who are available to play more often than not, and switching out some younger players in the back half of the roster for more polished, established professionals would make a difference, I think.