Depending on your assumptions, we could get away with three signings or need twice that. I think it depends on three factors:
If Jack goes. I'll be shocked if he stays but, if he does, he doesn't need replacing.
Tom Heaton. If he'll be back after four matches, that's alright. I'm not comfortable with relying on Nyland or Steer for the whole season though. Would Reina come for another year?
Can we buy a quality centre-forward (e.g. Tammy) for less than 40 million. If we can, that's a priority IMHO. If it's crazy money, we might have to spend it on the other positions like central mid.
So definite positions (IMHO): centre-back, central midfield, winger. Starting line up of e.g. Heaton, Targett, Ake, Mings, Guilbert, Grealish, Luiz, McGinn, Ndombele, Benrahma, Wesley. (Just picking Ake, Ndombele and Benrahma as examples. Pick your own if you like.)
If Jack leaves: those three, plus a replacement (4). Say Buendia or whoever.
If a Tammy Abraham is available: those four, plus the new forward (5)
If a goalkeeper is needed: those five, plus Reina (6). Starting line up of e.g. Reina, Targett, Ake, Mings, Guilbert, Buendia, Luiz, McGinn, Ndombele, Benrahma, Tammy.
There's a big difference between three and six signatures, and that's before we talk about adding depth in left-back etc.