Same Store On Two Different Url's

I have just completed a migration from one domain to another with CS Cart.

I was wondering if its possible to have the same store running on two domains...

I don't mean two installations with two db's of CS Cart but a single installation usable on two separate domains. I also don't mean a multi store.

Basically I want the same theme, same branding, same stock on two different domains.

When some one orders they can log into either domain to view their account and also from an admin point of view the same...

From what I can tell this is not possible as the store front url is stored on DB and this causes which ever url which does not match this to show as 'store unavailable'.

Thank you in advance.