When all you have is a hammer, it's the tool you always use.
That to say, apologies for always defaulting to Drupal, but as I know it best, it's the one I can think of.
The Organic Groups functionality of Drupal is more or less for this purpose. You would just create regional groups and people would be members of the site and then as many groups as they are members of.
It is the software running Drupal Groups which has thousands of groups.