I am running Apache witha redirect rule like this:
RewriteCond %{HTTP_HOST} ^1st-domain\\.com RewriteRule ^(.*)$ http://2nd-domain.com$1 [R=permanent,L]
On multisites such redirection works for me for empty requests :
RewriteCond %{HTTP_HOST} ^1st-domain\.com$ RewriteCond %{REQUEST_URI} "^/$" RewriteRule ^$ http://3rd-domain.com/ [R=permanent,L]