I would see what the requirements are for corporate strategy roles. If most, if not all, require an MBA then get an MBA. If most require a graduate degree, just make sure you show business savvy and commitment to the industry. I would also speak to a consultant about some of these questions; they could probably give you some additional clarity.
From one prospective law student to a practicing attorney, I wish you the best of luck!
From one prospective law student to a practicing attorney, I wish you the best of luck!