As has already been stated; You will need a dedicated server (or a virtual dedicated server) to install and use an alternative HTTP server, or other persistent process.
Unfortunately, DreamHost does not directly offer such services at the moment. They do have a partnership with hosting.com to offer dedicated servers etc, but the prices are not the cheapest available, so I would suggest shopping around if you are really interested in purchasing.
Here is a link to the services offered through the DreamHost / Hosting.com partnership.
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