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


umask(0);

if ($_SERVER['HTTP_HOST'] == "newdomain.com" || $_SERVER['HTTP_HOST'] == "www.newdomain.com"){
$_SERVER["MAGE_RUN_CODE"] = "website_code";
$_SERVER["MAGE_RUN_TYPE"] = "website";
}

/* Store or website code */
$mageRunCode = isset($_SERVER['MAGE_RUN_CODE']) ? $_SERVER['MAGE_RUN_CODE'] : '';

/* Run store or run website */
$mageRunType = isset($_SERVER['MAGE_RUN_TYPE']) ? $_SERVER['MAGE_RUN_TYPE'] : 'store';

Mage::run($mageRunCode, $mageRunType);