Multisite wordpress

Hello Support,
I need to set up a multi site installation. It's a nonprofit organization with 7+ locations. Each site is going to use the same theme (I'll be using one from rocket theme). And, I will probably be tweaking the theme quite a bit. Is it possible to have the one tweaked theme for all the sites or do I need to tweak the theme for each site? Another way to put this is - can I tweak the theme on the network level that is used by each site? Thank you, Carol