Is there a possibility to recover rewritten backup copy of an iPhone from iTunes?
Perhaps


If you do an iOS upgrade via iTunes and haven't backed up the phone locally "in a while", iTunes will do a backup and include the date and time in the name, so it won't overwrite an existing backup. You can see these backups in Preferences… > Devices. I don't know when iTunes decides to do an automatic backup, but that's a place to look.
The backups are stored in ~/Library/Application Support/MobileSync/Backup on a Mac and \Users\(username)\AppData\Roaming\Apple Computer\MobileSync\Backup\ on Windows 7, so if you back up that directory, you may have the desired backup on your backup device/service.


If you don't have the desired backup in either of those places then it's no longer available.