Using @Pro28 's example, getting MS from UPenn through Bryn Mawr College’s 4+1 program may not give all the management consulting interviews in NY that getting BS from UPenn gives, but it can give some. BS from either college will give plenty of high quality engineering job interviews. And the college name’s help or MS degree’s help ends at that point.
By the way, Bryn Mawr’s programs only add one year so MS might be worth. especially its program with CalTech that used be even funded.