As far as I know (and certainly I could be wrong) you can only have residency in ONE place at any time.
As for what it takes to establish residency, it depends what you're talking about. As far as each state goes for tax purposes, usually it's having a mailing address, change your driver's license, and register to vote. Register your car in the state if you have one. For schools, however, that gets a bit stickier. Some schools, if you move to the state for the primary purpose of going to school there, will always treat you as an oos student. Some schools (UMDNJ I think) say as long as you get an in-state driver's license you are an in-state resident and qualified to have in-state tuition.
The bottom line here is what is the driving purpose behing establishing residency? For tax purposes or for school? If for school, you'll have to check each school's rules. Sorry.