There is no realistic way to make room for Bregman and stay under the cap without doing 22 M, maybe even lower.
Here is our expected CBT Payroll: $243,842,334
If we trade the full salary of Pressly and Caratini it puts us at 223 M. That would leave only <18 M to sign Bregman. We'd need to move Dubon's 5 M and then we could afford 22 M (more like 20 M to have a tiny bit of wiggle room). But that present another problem, we do not have anyone else on the roster who can back up Pena. I don't think Dezenzo, Whitcomb, or Leon could do the job. Matthews isn't ready. We'd have to trade or sign a back up. Even if you go super cheap for someone like Nick Ahmed (+ defender), Luis Guillorme, or Ildemaro Vargas they'll put you over the tax threshold again.
The only option to get truly get under means moving Altuve, Walker, Hader, Valdez, McCullers, Alvarez, or Javier. That isn't going to happen. Or should not happen to make room for Bregman. Crane will need to pay the tax if he wants him back.