You have to a minimum of three years of experience doing physicals for the FAA then apply to be a Senior AME. As with regular AME's, they limit the number in a geographic area based on the number of pilots served.
The FAA also has a minimum number of exams per to continue to be an AME. Of interest, half of the AME's perform fewer than 25 exams per year while there are only 3% who perform over 500 per year.