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?"