Even a FFL can't build a full auto for his own enjoyment.
Actually, he can if he has an 07 FFL (manufacturer) and a Class 2 SOT (Special Occupational Taxpayer). The full auto gun then can never be transferred, except to LE or military, or to another FFL/SOT who has a demonstration request letter from a LE agency. It cannot be converted back to semi-auto (once a machine gun, always a machine gun under current US law). If it is not otherwise legally transferred and the FFL gives up his/her license, it has to be destroyed.