It's not possible to open multiple terminals in Edison through the serial port. The Edison's terminal communicates to your PC through a serial port. If you open one terminal session, you are opening and using the serial port. But, when you attempt to open another terminal session you will get an error message because the serial port is already in use (by the first terminal session), so you won't be able to have multiple sessions open.
However, you could have more than one terminal session through SSH. When using SSH to open a terminal session, you are using the IP address instead of the serial port so you wouldn't have the limitation that the serial port has.