My info may be outdated, but my father was an Air Force Health Professions Recruiting commander at one point in his career, and I asked him that question. Transfering branches is possible, but difficult. Every branch has a certain number of slots for each specialty, and within those specialties, a certain number of slots for each grade(O-1 through O-6, for example). In order to transfer, first you must be finished with your commitment to your current branch. That is, you can't owe them any more time for any reason. Then, the branch you are transfering into must have an opening in your specialty at your paygrade(i.e. Pathology and O-4). Not an easy match to find all of the time.
There may be exceptions to this, and don't take this as gospel; like I said, this is a bit outdated. Hope this helps!