Switch WP-domain after signup with Multi-Domain installed

One of my members created his blog at name.domain1.com but now he/she wants to cange it to name.domain2.com. I'm using the Multi-Domains plugin and both domain1.com and domain2.com are selectable at signup. How do I make that switch, so that the main domain is changed, but not the subdomain/blog name?

I don't want to ask my user to sign up a new blog since he/she has done alot of blogging on the current domain.