We require two options in our ~/.screenrc to do this:
multiuser on acladd nathan,root
The multiuser line tells screen to enable multiple users on all screens this user launches. Then we use acladd to give full permissions to root and nathan to this terminal. However screen will have to be suid root to work for non root users.
You can also issue these commands from the ^A: command line to get this at runtime without having to restart screen(1).