Elite Dangerous uses the email address attached to your account to determine which commander is accessed.
Adding a new purchase to your existing account will not give you a second commander. This means if you do wish to have more than one commander you will first need to make a new Frontier Store account with a different email address.
After you have created your second Frontier Store account, log into it through the Frontier Store and purchase the access you wish for the new account.
Once this purchase has been confirmed, you can then use your launcher to log into the new account with and play. If you already logged in to the Elite Dangerous launcher you will need to log out of your main account first. Under the options menu select "log out" via the launcher and you can then log in and play using your new account.
Please wait... it will take a second!