Boeing could produce up to 53 B-737 Max aircraft per month
However, FAA authorization is required, which has imposed a limit of 38 units

Aviation giant Boeing's -737 Max production could increase to 42 per month as early as October for about six months. It could then reach 53 aircraft per month by the end of next year, Bloomberg reported. The increase comes amid a surge in foreign orders, particularly from airlines in China, Uzbekistan, and Turkey.
Before increasing production, however, Boeing will have to meet with the Federal Aviation Administration (FAA), the US government agency responsible for regulating and overseeing all aspects of civil aviation in the United States: the manufacturer will have to convince it that it can produce more aircraft than it currently does while maintaining the same quality and safety standards. The FAA had established that the manufacturer could build a maximum of 38 aircraft per month. The limit was imposed after an accident involving an Alaska Airlines Boeing aircraft (see AVIONEWS); during takeoff, a door detached from the fuselage. "The FAA will continue to oversee Boeing's manufacturing processes and will work with the company to determine whether it can safely increase production", the agency stated.
AVIONEWS - World Aeronautical Press Agency