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This issue falls under the "Corporate Practice of Medicine" laws.
Maine (like many other states) does not have a specific statute regarding this, and is one of the few states that would allow a non-physician to own a medical practice. However, I would highly recommend receiving legal counsel to assist you in setting up this practice.
Here is a well written summary of this law (pulled from this publication: https://www.healthlawyers.org/Archive/Program%20Papers/1996_AM/[1996_AM]%20CORPORATE%20PRACTICE%20OF%20MEDICINE-%2050-STATE%20SURVEY.pdf)