Domain Mapping Plugin with a Mapped "www" domain

I am using WP Multisite 3.5 with subfolders and the Domain Mapping plugin on http://mydomain.com. I would like http://mydomain.com/newsite to be mapped to http://www.newsite.com (note the "www").

Currently, when I visit http://www.newsite.com, the url is rewritten to "http://newsite.com".

Is it possible to use the "www" on a mapped domain when the main site doesn't have one? Maybe via .htaccess?

Thanks!