It is possible. A post-residency physician can join the military and train in a new field. But, that person won't be eligible for an inservice residency immediately - application via the GME selection board is necessary, which takes time, and additionally requires endorsement from the command. This may or may not be given before that first staff tour is up. (The CO is certainly not obligated to endorse an application to leave early for training ... and they know that if they do let someone go early, they probably won't get a replacement.) Then, there may or may not be training slots available in the desired specialty, and the person may or may not be competitive for a slot. In the military, there's more to being "competitive" than just grades and board scores and LORs. This is a fairly complex process.
If the stars aligned just right a physician could join, apply in September for residency the following year, and conceivably get a spot. More likely, that physician will spend 2-3 years practicing the first specialty before having a realistic shot at a second residency in the military.