I've installed Domain Mapping and it works ok (mapped externaldomain.com to this.internaldomain.com).
The only issue is that the Theme is looking for files on the mapped url - and getting 404s. E.g. the logo is in internaldomain.com/wp-content/themes/images but the newly mapped site looks for it at externaldomain.com/wp-content/themes/images - and it's not there.
I feel it might have something to do with nginx, but not sure.
Thanks for the help!