I think the Master's degree may be specialty dependent.
For example, for a specialized field such as Rad Onc, I can imagine a Master's degree in physics, related to Rad Onc would be helpful.
I can imagine perhaps a Masters in Physical Therapy be helpful for Physical Medicine & Rehab. I don't know if a Masters in audiology or speech therapy would help for ENT since ENT is so competitive.
If you are planning to follow a research path and applying to very academic, research-oriented programs, I am sure a Master's or a Ph.D. in a related field can be helpful.