Repeat the authentication code for each access type giving each their own name to reflect the level of access you are filtering for.
Leave the fail redirect blank for all but the last on that appears on the page so that the next one will check after the one before fails down the line.
The other option is to use DataBridge instead of MySQLi Server Behaviors. That would allow you to save the access group as a session variable during login and then define access rules based on the session variable value instead of using separate authentication server behaviors.