Or 4 parallel runways like Detroit Metro (KDTW): 4R, 4L, 3R, and 3L.
In fact, taking this dodge into account, the DFW example I gave actually has five parallel runways; the two they label 18/36 are actually the same heading as the three they label 17/35. I wonder if they'll ever need to go to six and add an 18/36C.
Doing that for 4 would need one direction to be A B C D and the other to be B C D E (which is workable, but doesn't seem particularly more elegant than just using left, right, and center [and in fact is worse in some ways, since from one direction, B is the left-most and from the other, it's A])
There would be no (or extremely rare, at a minimum) operational reason to alternate directions for takeoff and landings on parallel runways. (There are rules for simultaneous operations to parallel runways and having them be in opposite directions would be problematic as you have to assume some aircraft will execute a missed approach and would then be climbing into opposite direction landing traffic with only a small lateral offset.)