I always use staging subdomains for my main domains to test beta versions of website or create a new one while not affecting the love version.
I always have the existing domain ftp in my site manager but I would like to connect to that and then change the dir and then be able to save the site as staging.domain.com
From the Site Manager, right-click on your existing site and select "copy", this will create a duplicate of your existing site. now rename your copied site profile to a new name that suites your needs.