I did try creating a second website, copied the Web Interface folder, and recreated the IIS applications pointing to the new copy of the folder, but used the same App Pool identities as the existing ones.
This did not really work. I was able to get into the new site, but I could not also access the other site (ASP.NET Core error about more than one application in an app pool not supported) at the same time. And, any changes I made within the "new" Config portal were reflected in the "old" website.
If I use different App Pool identities, would that make a difference? Is the site configuration information stored in the database based on the app pool identity or something else? Is there a way to tell the Adaxes service the new application is using a different hostname?