Your not likely to find a fleet owner that will let his equipment sit idle 50% of the time...if your looking to drive for somebody else.
If you have cash to buy your own truck, you could possibly make it happen, depending on where you live and what company your leased to. I still doubt that it would work out very well though, especially if you want exactly one week on, one week off. In this business, you seldom know where the next load will take you. Your not likely to be within a reasonable distance of home on any particular day. It may be a week...or a month....or longer before you find yourself close enough to deadhead home. If you start deadheading more than a couple hundred miles every other week, your gonna find yourself working for free if your not careful.
The guys who live in certain parts of OH seem to get home the easiest. With some carriers (like Load One) living in MI or northern OH is a pretty sweet setup. A lot depends on the carrier.
One option you might find (but it would be like finding a needle in a haystack) would be to find someone else who wants to be off every other week and work out a schedule....but then ya still gotta get the loads that keep ya close enough to make it workable.
It's a VERY long shot in this business...in my opinion.