I was able to get this to work! This question was helpful for me to see when I was initially trying to get this setup to work, so I wanted to come back and add an answer in case it’s helpful to anyone. Here is our final setup:
User-facing URLs are like these examples:
– mainsite.example.com
– secondsite.example.com
– thirdsite.examplecom
In WP Multisite, mainsite is the top level site, with the others as subsites. We are using a *subdomain* setup (not subdirectory). In the Network Admin part of WP Admin for Multisite, I set their URLs to each URL above. Our DNS routing points these subdomains back to our host.
*Note: the DNS entries for the subsites are actually CNAMEs in the form of secondsite.mainsite and thirdsite.mainsite. So I have CNAMEs for example.com directing to our intermediary that maps the sub-subdomain URLs to the host and WP Multisite setup. (This is all a bit confusing, honestly.)
I had to update the main (top level) site URL following these directions: https://wordpress.stackexchange.com/a/334109
Then I had to update wp-config.sh for the top level site to match:
define( 'DOMAIN_CURRENT_SITE', 'mainsite.example.com' );
Finally, I had to mess around with our Google login plugin settings to allow SSO into each WP Admin site via Google. This was the final edit I needed in wp-config.php:
define('COOKIE_DOMAIN',FALSE);