Of course you can license code you don't own. Otherwise there would be no way to have a license that allowed its recipients to redistribute and then allowed the people who received the code from them to redistribute it themselves.
I'm afraid you don't really understand licenses. A license like BSD gives you the rights to distribute the software subject to certain provisions. It does not give you the right to change the license. I can't really spend any more time on this but I'm sure people around you can point you in the right direction.
