Is it possible to ask 2 professors to write a joint-letter of recommendation? I have been working with 2 faculty members on the same project. I took a class from each of them, and the three of us meet in person on a weekly basis. I think it's reasonable to assume that they've seen the same level of research ability from me. 

I am planning on applying to graduate school, so I was wondering if it's appropriate to ask them for a joint letter? My motivation behind this is


the two of them mentor me on the same project, so 2 separate letters may have unnecessary overlap?
applications typically require 3 letters (I already have 2). For schools which you can submit > 3 letters, I would think they still value quality > quantity
may be slightly less work for both of them (?)


I don't want to come off rude by asking the two of them to co-write a letter of recommendation for me. Is it generally deemed appropriate to ask two faculty members to do this? I think this is quite uncommon because on applications I only get to designate one writer per letter of recommendation (i.e. provide just one name, his/her title, email, phone, etc). If so, how should I phrase the question of asking both of them to co-write a strong letter of rec for me?
I have received applications that have had such a letter in them (well, at least one).  It came from a lab director and the applicant's immediatiate postdoc supervisor in that lab.  I thought the letter conveyed the student's experience in that lab very well, provided a nice bottom-to-top view, and it was more clear than if it were two letters, as I didn't need to put the connection between two letters together in my own head.

The letter did not raise any eyebrows, and it seemed entirely appropriate to me.

It's probably not the right thing to do more often than it is the right thing to do, but when it's right, it's right.

To directly answer the "how do I ask" question, something along the lines of "given the limit on the number of recommenders allowed, it occurs to me that there may be certain advantages to getting a joint letter from you and Dr. X, especially because ... [reason goes here].  Do you think this is an OK approach, and are you amenable?"