5 of 8 Editing to be more general and perhaps on-topic, hopefully OP is ok with this :)

Can a U.S. President have a non-government owned aircraft that would routinely be given the call sign AF1?

Can a US president use a personally owned jet with the call sign AF1? Would the Air Force be obligated to add security and defense measure to this aircraft if the president refused to fly in the VC-25?