Staying logged in between sites


I am building a multi-site which will be like EDUblogs. I also want to create another multi-site network for a Buddypress network which will have learning management features and social networking.

I don’t want to combine buddypress with the Edublogs-like site because I think it will get too complicated and more problems may arise. I would rather develop each separately so that I can use the basic functionality if the buddypress setup causes problems.

Is there a way that someone who is logged in as a member of the EDUblogs-like site can automatically be logged in when they visit the Buddypress network of sites? Can they be integrated even though they are on two different multi-site networks?

Or is there a better way?