Create one feed out of several Drupal feeds?

I have a multi-site Drupal installation. Each multi-site is a subdomain of example.com (like ms1.example.com, ms2.example.com, etc.)

Now, the homepage (http://example.com) is not run by Drupal, but I want to insert a feed, which consists of a mash-up of several selected feeds of the subsites. And this new feed shall not have the URL of a subsite, but the URL of the homepage (where no Drupal is installed).

Example:

the feeds

• sub1.example.com/new-nodes.rss
• sub2.example.com/feed.rss
• sub3.example.com/blog.rss

shall become one feed at "example.com/overview-feed.rss" (although example.com is no Drupal site).

Is this possible? I don't want to rely on a hosted service, I want to do it with my own shared hosting account / server. (I'd prefer an Atom feed, if possible)