Hmm....I know this is possible, but I'm not sure how. Bank of Montreal (Canadian) for example, uses this technique. When I go to the main URL to do my online banking, I get forwarded to another server. That server may be bmo3 or bmo4 or bmo5 or whatever. The main server does load balancing (or perhaps it's just dumb round robin) and simply forwards off requests to other BMO servers.
The phrase 'round robin DNS' is on the top of my tongue, but I don't think that's it.