What follows is a field report I received from someone who successfully managed two offers without burning any bridges.
First, I would like to thank you for providing a lot of useful materials on case interviews. Although I was not looking for a consulting job, I ended up using your materials to prepare for a case interview for a business development job (the office was filled with ex-Bain consultants and they had exhausted all other tests, such as fit and financial modeling, on me).
Second, I cannot agree more with your advice on handling job interview schedule conflicts. Such situation actually happened to me just 2 months ago. At the time, I had received an offer to work as an ibank associate at a leading bank, but was still mid-way through my process with the BD position, which was my much preferred job. It was because the latter opportunity came about much later in my job-hunting process.
A relative, who's a senior executive at another leading ibank, advised me to take the banking offer while waiting for the business development one, I nevertheless felt very uncomfortable with such action. Also, I had a very good headhunter who was handling the ibank offer, and I knew if I did what my relative told me, I'd be burning bridges with not only the bank, but also this headhunter who had helped me so much.
Hence, I did exactly what you said. I was honest with both sides regarding the situation, and got extension from the bank while the BD position also expedited the process. This allowed the bank to hold on to their back-up candidate, so they would not be as upset when I reject their offer; I also showed the other firm how much I valued the BD position, so the building of my relationship with my current boss actually began before I started working here.
What's to note is that under such circumstances, the candidate has to be prepared to answer tough questions from both sides and be prepared to be as honest but also as respectful as possible. For example, when I explained to the bank my situation, a few executives called me to probe the criteria I was considering, what more could they do to ascertain my acceptance of their offer, etc. It's difficult for me as I was certain to take the BD offer once it came about, regardless of the size of the compensation package. Fortunately I had the headhunter to help me with negotiation, and I think undergrads / MBA graduates can enlist their schools' career counselors in this area.
Please feel free to share my story with other people if you see fit. Thanks again for all your career advices!
Very well done, and a perfect example of not burning any bridges, but still getting what you want.