My class III items are under a MO LLC. The LLC itself is the applicant in the ATF's eyes and you MUST have a C&R in the name of the LLC. I actually hold 2 C&R licenses, one in my proper name (mr. JsARCLIGHT) and one in the name of my LLC (JsARCLIGHT LLC).
I am the only member of my LLC so I am the only one who is authorized to use and store the weapons. It is my understanding that any member of the LLC may legally operate the weapons without the other members around, but the weapons MUST be stored at the address of the LLC only.