How many people can help treat a disease?

Related to some of the other disease-based questions here, I have one that’s not covered: how many people can attempt to treat disease on a player using their Heal skill?

My reading of the rules suggests at most one, but I’m not sure.

If so, can others use Aid Another for this individual during the course of the extended rest?

To me, logic suggests that too many people being involved might actually make it harder to treat the patient, i.e. the classic “too many chefs in the kitchen” argument.