From what I've read to various blogs, in case you applied for a graduate programme and for more than one MBB offices, your number 1 choice will send your application to your 2nd choice, in case it considers that you don't fit. That may be because they have better applicants than you for their office, but they still want to give you a chance, so they send you to your 2nd choice. The 2nd choice again will follow exactly the same process, but only if they do need any applicants. In my case, I got rejected by my 1st BCG choice (London) for the above reason and the 2nd choice (Athens office), because it's a small office and they don't have open positions (at least that's what I was told by the local recruiter).
In case you're accepted by your 2nd or 3rd choice, the rest of interview process will be for that particular office only and you cannot negotiate a transfer. This is the strategy at least for McKinsey, as I was told by a recruiter who works for their London office. You can negotiate a transfer after 2-3 years, when the entry-level position period comes to an end, but still no one can promise to you that you'll be transferred, because it depends again on the needs of each office.
I'd like we have here though the opinion of someone who've worked for an MBB firm.
All the best