I've moved a network from one server to another today, which also involved changing the domain. I'm on Dreamhost.
The error message goes something like...
The webpage at http://domain.com/wp-signup.php?new=domain.com as resulted in too many redirects. Clearing your cookies for this site or allowing third-party cookies may fix the problem. If not, it is possibly a server configuration issue and not a problem with your computer.
This happens whether I use the www or not. The domain (in Dreamhost's settings) is set to "Leave the www alone" and so are all of the subdomains.
I've checked the wp-config file. The DOMAIN_CURRENT_SITE is set to the domain without the www. It's identical in the site's wp_options site url, home, and wp_site in the database.
I copied a fresh htaccess to try that, and even deleted it to see if it was somehow causing a problem. That didn't help, either.
And, I cleard my cookies and flushed my DNS. Then thought about MAKING some cookies in hopes that the break would do me good.
I can give the url if it'd help.