Why for instance do we need 3 medical services complete with a whole chain of VSO's? An injured serviceman is not going to care what colour of uniform the medics are wearing or which band the stretcher bearer plays for in his day job!
You could call it a Defence Medical Service, and use all 3 Services in each others healthcare centres, but ask each Service to lead on a certain medicine type (Diving/Nuclear Medicine, CBRN and Aviation perhaps?).
You could also pool the requirement for consultants across all 3 Services, with slight weighting for specific tasks, but with all 3 ready to support each others specialist tasks.
The DMS could be commanded by a single 3* chosen from across the Services, with a Service lead at the 2* level.
How does that sound as an idea?