You should set up a second account. If you only want to use the address you currently have, then just set it up using a disposable alias - anything accepted by the system is fine. This new account will be automatically added to your billing group.
Once the second account is active, go to the Remove Addresses page. Select "Send to Another User" for the address or addresses you want to split off. In the text box that appears, enter the address of the new account you created.