They COULD do it, but there are just too many suitors out there and not enough supply. Brezzz would have to have the deals in place right away and possibly overpay for each guy to get them to sign before other teams are involved.
With Masa on board, I think they are kind of stuck at the DH position this season. They could possibly DFA him next year and only eat one year of the salary or move him at this deadline if he's performing well.
C Narvaez
1B Okamoto
2B Story
SS Mayer
3B Bregman
RF Anthony
CF Rafaela
LF Duran
DH Yoshida
Bench: Wong, Refsnyder, Hamilton, Romy
Sox have said they want to turn the defense around. Not sure how they go about doing that with Story at SS. The logical move is Mayer to SS and Story to 2B. Bregman was decent at 3B and they clearly like his fit so they prioritize him over Schwarber and other big bats. To help the IF defense, they then target Okamoto who can also provide some RH pop and maybe some comfort to Masa. They deal Abreu instead of Duran in a package for a middle of the rotation arm. They stick with Duran because he stays in the lineup more and can backup CF if Rafaela needs to move to the IF in an emergency. They also believe in Anthony's glove in RF.
Hope for health luck with Breggie, Masa and Oka to become fast friends, Anthony to have no post injury issues and Duran to return to a 120ish wRC+.