Okay, read this first then double-check the DNS settings.
https://premium.wpmudev.org/blog/domain-mapping-wordpress-multisite/MyAARPMedicare Login
Your domain name settings in the WordPress site addresses need to be set properly. All three will point to the new domain name.
I usually just use a Cname record for the ‘wwww’ instead of an A record for the www (machine name) version of the domain… unless I need a different server for the machine name but a Cname is more intuitive in my thinking. Quicker fix if it ever needs changing also.
Thanks a lot for the great information. I was looking for the same and finally got my answer!
