Is it possible to ask 2 professors to write a joint-letter of recommendation?

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?"

To be honest I have never heard of such a thing. Even when getting letters from professors who co-advise all their students (such as husband and wife profs), I have been given distinct letters.

I would recommend picking one of them. If in their letter they were to say that they're working with you along with Professor Plum and the letter writer believes Plum shares his/her sentiment, that would be fine. But co-signing does seem very unusual.

PS. If you were applying someplace that required exactly one letter, there might be some stronger case for combining them. Given that there are 3 but you've already allocated 2 of them, I think it would be really odd to try to have the 3rd cosigned: it's like you're cheating to get 4 people to recommend you when you're allowed 3.