Sometimes there is what's called "Secondary Domains" which actually create a virtual host record form the shared hosting account's control panel. This is how Nexess shared Magento hosting works. If you're host doesn't support real virtual hosts, I would find a new hosting provider or get a second account for the second site, assuming they aren't running on the same base.

Sometimes there is what's called "Secondary Domains" which actually create a virtual host record form the shared hosting account's control panel. This is how Nexess shared Magento hosting works. If you're host doesn't support real virtual hosts, I would find a new hosting provider or get a second account for the second site, assuming they aren't running on the same base.

Edit: One thing else to consider... An actual virtual host is required to have an SSL setup on both domains. It's not possible with anything else because each one requires a dedicated IP for SSL negotiation.