I'm wracking my brain trying to come up with one example (any industry) of where a company is purchased by PE and as a result voluntarily downsizes, even if it comes with improved margins. I'm doubtful BB will be the exception.To me these are the options. Go to a niche, high quality, classic shop or just call it a day.
One thing I think it likely is that we won't see better quality, I think those days are long gone. Better/worse/same quality, the move after any restructuring/sale will be to cut costs. So I expect the bricks and mortar footprint will shrink considerably, along with the associated jobs.
Tailoring/alterations/handiwork will be even more centralized, and while physical locations will shrink it's a long shot hope of mine that a few of their experienced and skilled tailors will remain. As far as product offerings they could use a significant shot of creativity (a la perhaps a Paul Stuart model or better yet to get lucky on a rising star who makes good), but those goods will almost certainly come from overseas manufacturing.
And while stable items like OCBDs and non-MTM suits are already non-US produced I can see those remaining somewhat unchanged, I'd love to see some of their trad clothing updated with more contemporary materials, such as the more knit-like shirting that Uniqlo uses in their shirts, that are non-iron with a bit of stretch.
Or a "BB version" of those tech fabric suits that everyone else is selling, but with pants that have a proper crease versus these others that look like chinos.