It's not an official prequel, but a German film called Requiem by Hans-Christian Schmid and writer Bernd Lange is going to leave off where The Exorcism of Emily Rose picked up. Inspired by the true story of Anneliese Michel who died in Germany in 1976 after ten, grueling months of weekly and sometimes bi-weekly exorcism sessions, Emily Rose told the story of the court trial to determine who was responsible for the young woman's death. Requiem describes the events that led up to the exorcism and tries to answer the question: why would anyone put themselves through that?
This website does a pretty good job of answering that question too by recounting the life of the real Anneliese Michel. If Requiem is at all faithful to actual events, it's going to be a very disturbing movie.