Didn't they make a 9x19 conversion kit for the M3A1?
Rather than rely on an aging memory, I consulted my firearms library for documentation. In one of my books about military weapons, it was stated that the original M3 design contemplated being able to convert the M3 submachine gun from .45 ACP to 9mm Luger by swapping out the barrel and bolt and adding an adaptor to the magazine.