How can a new state join the union?

It is currently impossible for a "new" mainland area to join the union unless one of the forty-eight states split in half and charter as two separate states. It is possible however for an existing populated land mass to become U.S. federal territory (Commonwealth), as is Puerto Rico. Were this to happen, the people of the land mass at issue would have to relinquish sovereignty and swear to uphold the constitution of the United States of America.