Hmmm...not sure why there aren't more replies. I don't have a formal arrangement with anyone. I'm one of several back-up doulas that another (very experienced and very busy) doula calls on if two moms go into labor at the same time. I'm in a small natural birth-friendly community, so many of the doulas pretty much either know each other or ay least know OF each other; if I had two moms in labor at same time, I feel certain I could find one willing to help out/step in as a back-up. My client load is small enough, however, that it's not likely to happen (hasn't yet in two years).
I did know of two doulas who partnered for awhile; they held group interview meetings (more of an informal "come and meet us and ask your questions" kind of thing). If hired by a couple, they were hired together, with the couple knowing that they rotated every other birth to more adequately ensure a "fresh" "rested" doula.
The only exceptions were repeat clients; in those cases, they tried to have the same doula attend if that's what the client preferred. As far as I understand, the deposits were split, and whichever doula attended the birth received the reminder of fee and also did the postpartum visit. Hope that helps!