Provided you do not need an ssl cert for each domain it is relatively straight forward to create a multi-store setup. If you host with Dx3webs we will do this for you .. simply raise a ticket.
1) configure magento.
In system > manage stores
Add a new website, store and store view for your new site. Remember the code for the website.
2) Create a domain alias for you new domain pointing to your existing domain.
3) Add a little logic to index.php