Multisite Redirection to new domains

Try adding something like the following at the top of your .htaccess file:

RewriteCond %{HTTP_HOST} ^(www\.)?oldone\.com
RewriteCond ${REQUEST_URI} !^/wp-admin
RewriteCond ${REQUEST_URI} !^/wp-login
RewriteRule . http://newone.com%{REQUEST_URI} [R,L]

Make sure the browser cache is clear. Change to 301 (if that is the intention) only when you are sure it’s working OK.

Repeat for any other oldoneN.com / newoneN.com combos, unless there is a pattern with the domain names?

Alternatively, if you never want to redirect /wp-admin or /wp-login etc for any domain then you could include an exception for these URL-paths. Although that would probably interfere with some of the other MU directives.