I know that MIT's LFM program (the dual-degree Master's in Engineering + Sloan MBA) brings in about 1 PhD in every class of about 50. For example, last year, one incoming woman had a PhD in Physics from Harvard. Two years later, another incoming woman had a PhD in electrical engineering from Stanford. You'd think that somebody who already has an elite engineering PhD would have no interest in picking up an engineering master's, but LFM allows you to get that master's in some other engineering discipline. For example, you could come in with an EE background and decide that you'll get your master's in ME or ChemE or whatever.
Incidentally, the other way around has happened too - every year or so, 1 or 2 students will use LFM as a launching paid for their PhD. Usually these students will stay at MIT after LFM to get their PhD. For example, Randal Pinkett, who won the reality show Apprentice 4 (the one with Donald Trump), after graduating from LFM, stayed at MIT and got his PhD from the MIT Media Lab. Others have stuck around to get PhD's in engineering. Certain others have gone over to get doctorates at Harvard (especially Harvard Business School).