I don't think it will make for the best team to keep all four. I think it really comes down more to 3, Tatum, Brown, Hayward, all natural wings. Kemba Walker is really more of a PG (albeit of the scoring variety) and we need to keep him and Smart can do it all and we will keep him as well. We simply can't afford to pay for 3 near max level wings. It doesn't leave enough to fill out the rest of the team.
I feel that something will have to give. The best scenario for the Celtics is probably to get a trade for Hayward for a legitimate starting level big. I know there are issues with this regarding doing right by Hayward and also any trade is easier said than done but this would be the best for the Celtics.
You consider trading Brown or Tatum as well but only for very elite young bigs (such as when Davis was being pursued). I think that type of trade is even less likely.