Changing the domain name of a WP multisite installation?

Hi,

I’m sure this question has been asked before but I can’t find any answer that really addresses my needs …

So, I’ve got the following situation:

WordPress 3.0.1 on Windows Server 2008.

A multisite WP installation running on symposium.local.net with several subsites: symposium.local.net/site1, symposium.local.net/site2 etc.

Everything is running perfectly right now.

BUT I need to enable access from the Internet to this network of sites too now so I need to ‘apply’ a public base domain name to it (symposium.mysite.com).

How would I do this? I tried several things already but it didn’t really work out …

I’d really appreciate a step by step explanation.

Thank you very much ??

Jerome