Multiple installs, shared themes…possible?

I’m setting up multiple WP blogs, one in each folder like this:

teams/red/
teams/white/
teams/blue/

Since the ‘themes’ folder is located under each blog’s wp-content folder, can I move the ‘themes’ folder to the root of my ‘teams’ folder and have it be shared among all the blogs?

This way I won’t have to duplicate numerous themes for each team to pick from within their own area. Is there some path string in one of the PHP files I can simply modify?

TIA,
Sandd