Procedure for having multiple advisors for a PhD thesis Assume that one has begun a PhD program at a university which allows a student to choose an advisor after his/her first year in the program and the student has narrowed down to a couple of potential advisors and that he/she wishes to do his thesis under multiple advisors.

What is the procedure for suggesting multiple advisors? Whom do you speak to first? What if the advisors don't go so well together?
Unfortunately, I think the answer is going to be - "it depends"! I have advised several graduate students, including 2 who are currently "co-advised" with other faculty. In one case, the student approached me first, but I already had a working relationship (co-teaching, serving on supervisory committees together etc.) with the other faculty member. In the other case, I was approached 2nd, and again, I had previously worked with the other faculty and knew them well. When talking with potential students, if it is clear that a different faculty member would have better or equally relevant expertise, I always suggest talking to them. However, that's my opinion. I also have colleagues who would flat out refuse to consider co-advising a student. 

I think the key "test" is to imagine your dissertation work as a 3 way collaboration - what does each faculty member bring to the table? What are they going to get out of it? How you approach them is completely dependent on the individual personalities involved. You should also find out if there are any policies on co-advising at your institution or department - there are none at mine, but that might not be universal.