The empowered healthcare manager refuses to let one employee bully another. If they have a bully on board, they warn, reprimand, then terminate. Their reaction is swift and decisive.
When the bully is a customer, it's no different. A bully is a bully regardless of what end of the transaction they're on. To the staff, being bullied feels the same.
There are those in this world who go around testing the rest of us to see if we will tolerate their incivility. Whether he's a patient, physician, or some other external customer, just because the bully has customer status doesn't mean he gets to assault your team. The empowered manager protects the herd, defends the front line, and shelters those without authority from those with it, those who consider it their license to be mean.
Of course, you go to great lengths to resolve any and all issues, but after all your Magic Customer Service Dust is spent, your spirit and that of your staff is bruised and bloodied, and the bully is still rabid, you treat him like you would any bully on staff. You warn, reprimand, then terminate.
Some customers just need to be fired.