Coincidentally, I was just researching this same scenario. Client has multiple domains they want pointed to the same website.
According to this thread at
Google Webmaster forums the correct method would be a primary domain, and other URLs should give a 310 http response.
Okay - I think therei s a misunderstanding on this.
There is nothing wrong with having multiple Domains for a single site.
Under the condition that only 1 of those Domains resolves directly to the site.
That means you should have a Prefered DomainName.
If anyone requests the Prefered DomainName, they should go directly to the site - getting a 200 response.
All the other DomainNames should point to the Prefered DomainName - using 301 Redirects.
Example:
You have 4 Domains;
mysite.com
mysite.net
mysite.co.nn
mysiteaswell.com
For various reasons - the .com domain is selected as the prefered DN.
That means the other 3 should all be pointed/redirected to it.
If I go to mysite.com - I should get a 200 response.
If I go to mysite.net or mysite.co.nn or mysiteawell.com - I should get a 301 Redirect response, and end up at mysite.com
If all those domains resolved to the same site/files/content - and all resolve as 200's, then that would be External Duplication.
What I have done on my account is have one folder in my public_html oritinally setup with one domain. Then all the other domains are made additional add-ons and pointed to the same folder. The response I get when i go to one of those URLs is a 301 and it displays the same site.
What I'm still looking for is whether or not to submit the sitemap multiple times under each domain name.