Hi Virgil—
Thanks for the question! If the two domains are to be hosted on the same server—which is, of course, necessary for a single instance of EE—then multiple domains are set up the same way, whether they’re both .com or .com.au and .co.uk. Essentially, what you would do is have your hosting environment set up the second domain to use a separate directory from the main domain as its own web root. In that folder, you would then follow the steps outlined here. All that to say, EE is completely agnostic when it comes to top level domains. As long as your host can serve web pages with it, EE can play nice. 😊
Does that help answer your question?
Kevin