I'd worry that SAAB just won't add anything to the portfolio.
I think it'd be quite clear-cut actually.
I *think* I'm correct in saying that Saab hasn't ever done a rear-drive model (the Sonnets weren't, were they?), so that's immediately a niche that BMW is unlikely to explore in any great detail (next 1-Series aside) and it's unlikely to impede on the "sport saloon" ethos of BMW.
Saab would still compete
mainly with Volvo - all cars are safe these days but Saab and Volvo still had a stronger reputation for it than any other maker, so that's one take. Saabs = safe.
The next is design. If BMW was clever with Saab and could achieve decent economies of scale, then it wouldn't cost much to develop really contemporary, simple, clean designs with a nod to the more unusual stuff Saab was doing in the past. Hell, make them all hatchbacks again. Audi has proven with the A7 that hatchbacks don't have to be low-rent. In fact, Audi is more likely a company Saab would compete with than BMW. I reckon with Saab gone a lot of old Saab buyers go for Audis (and Volvos) now, rather than BMWs or Mercs.
The main complaint of GM-era Saab was that they were getting blander and blander - so a design-led company, both inside and out, would be a good approach. And quality, obviously, which we know BMW can do.
And practicality: Another very Swedish characteristic. If you take the BMW Touring ranges, great cars, usually quite stylish, but not particularly special in terms of space - a Mondeo estate is more commodious than a 5-Series estate. Make Saabs practical, and you'd rope in the sales on that front too.
None of the above would really encroach on BMW's turf, yet with the right engineering it could make them loads of money.