Yup, there are lots of people who want more than just an MBA. It’s kinda crazy and kinda awesome. According to the GSB admissions website 15% of the class already has an advanced degree before starting their MBA. Another 20% of students are pursuing a second degree at the same time as their MBA.
There are a few options. A couple of degrees can be done successively (for example, many of the JDMBAs do two years at the law school then two years at the bschool) while others are done concurrently (the MAMBA degree, MA in ed & MBA, students take classes at both schools at the same time).
The options for joint and dual degrees at Stanford are: JD, MD, MA education, MPP (public policy), MS in Computer Science and MS in Environment and Resources (referred to as E-IPER). The application requirements are different for each program. For most of them you have the option to apply to both degrees at the same time (JDMBA). For some you have the option to apply once you are at the GSB (CS). For others you can apply at the same time or while at the GSB (MAMBA). I would recommend checking out the admissions site for some more info on the degree you are interested in.
There are also a bunch of students doing programs at other schools, including Harvard Kennedy School.
What are the pros of doing a second degree? Well, the big one is you get a second degree in an area that interests you. This could help with networking and getting certain jobs. You also usually pay less for the second degree than you would have had you done it separately (for example, if you get into MAMBA the Masters in Ed is basically free and if you do the JDMBA it’s four years total, cutting your JD tuition by 33%).
And the cons? For most of them, more time in school. Stanford is a lot of fun, so this could be seen as a pro, but at the same time if you’re ready to get back into the workforce it can be seen as a negative. In addition, you might need to take more units each quarter meaning you’ll be busier than your classmates with less time for the fun stuff like FOAM and BPL.