Multisite, multiple domains per site

In vanilla WP, a site cannot serve multiple domains like that unless it’s the root site.

Additionally, your desired setup would lead you to one of two situations:

  1. You’re succesfully serving the site on 2 domains, but all the canonical tags point to the first domain regardless of which is setup
  2. Google sees duplicated content and hits both sites with an SEO penalty

Which leads us to the SEO friendly, simpler more performant solution:

Set up your Host to redirect site3.com to site3-new.com, and only serve WP from site3-new.com. Any visitors to site3.com would get a 301 redirect to site3-new.com. This updates all the search engine results too.

You can do this via Nginx or HTAccess rules, but most hosts have a point and click option to do this in their hosting panels, even some DNS providers will do this for you.

Otherwise you would need to install a plugin for doman mapping. But this would be an inferior solution for your problem with various disadvantages.