SHEFFIELD, Mass. — A group of family members representing more than 50 people who died in the crash of Ethiopian Airlines Flight 302 are calling on the Federal Aviation Administration to conduct a full regulatory review of Boeing’s 737 Max before it is allowed to fly again.

The Max, which entered service in 2017, is Boeing’s most recent update to the 737, which was introduced in the 1960s. Because it was not an entirely new airplane, the F.A.A. reviewed only the parts of the Max that differed significantly from a previous version of the 737.

By certifying the plane with a so-called amended type certificate, the F.A.A. allowed Boeing to get the Max flying years sooner than it would have had the company introduced a brand-new plane that had to be certified for the first time.

But with scrutiny of the F.A.A. mounting after the crash in Ethiopia and an earlier crash in Indonesia, the families of many victims are calling on the F.A.A. to take an entirely new look at the Max. The plane remains grounded while Boeing works on a software update and other changes intended to make the Max safer.