Mirror domain on my wp

As you have seen, when someone enters your site with an addon domain, it thereafter uses the primary domain name. This is just what you want if the addon domain just corrects a typo, or you alias “thing.co.uk” and “thingie.com.au” to “thing.com”, BUT what if you want the various base domains to be retained. The usual answer is that when you do this you have duplicate content at different web addresses, and google don’t like this.
Maybe it would help if you described in more detail what you want to happen when your various domain names are used.