I created a new user and set their role to classified members
I then logged into the classified member user account and posted a classified ad
In the left side bar navigation, there are 2 "classified" headers.
/wp-admin/edit.php?post_type=classifieds seems to be a super admin menu. It displays in a table, the logged in users classified posts, BUT in the header, it displays
Mine (#) | All (#) | Published (#) | Drafts (#)
If the classified member user clicks on the "All" link, they are directed to a table listing all users posts. From their they can scroll over the title to surface a menu
edit | quick edit | trash | view
This allows classifieds member 1 to edit or delete anyone's classified posts