Maybe:

You're asking something of a hair-splitting question.
Yes you can own a 'business' that calls itself a medical spa.
No, you can not generally employ a physician.

The general way around this is that the physician forms a corporation and your corporation pays the physicians corporation to provide specified services. That way the physician can get paid and you have a little control over what's happening.

There is a flaw in this process for non-physicians.

Since the 'medical spa' will be operating under the physicians license and malpractice, there is no way to operate without the physician extending that to the business. If there is some interruption in physician oversight you effectively are shut down.

Do a search on this site around something like "American Laser Clinics And Armed Guards" and you'll see what I mean.

Hope that helps.