If all your incoming telephone lines are busy too often, don’t automatically add more incoming lines. They’ll tie up your "answerer" even more. Instead, add one or more lines dedicated for outgoing calls. Instruct all staff and doctors to use only those lines to call out, leaving the fewer main lines for incoming calls.
Only if all else fails to solve your problems with busy signals and answering hassles should you consider adding another incoming phone line. It will add to your costs, perhaps necessitating more phone answerers, but you can’t afford busy signals and non-responsive staff.