I would guess that ownership will just give their employee Mr. Atkins a mandate, such as:
1. field offers for these players, don't bother fielding offers for Vlad we don't want him dealt
2. any trade of player x, y, z needs ownership approval
3. any trade of players a, b, c only require Shapiro approval
The real downside is that there is nobody who has to capacity, ability, and freedom to make the big forward thinking moves.
To pull of a quick and decisive rebuild this team would probably need to trade Bo and also do very well in the trade. That is not going to happen. I mean it could happen in the offseason but by the trade deadline is such an awesome pinch point for sellers these days.