God knows I've notched many a purlin, most of them 6x6, and like Michal said, they were taken down to 4", with a 4" lap (of course, the lap length depends on the size of the principle rafter). But these were full 6x6, not 5.5 x 5.5; keep that in mind. And from what I understand about wood is that a 2" notch in a 6" timber still holds its weight distribution properly - the weight is transfered onto the principle rafter at the joint.
Also, what length are the purlins spanning? This wiil make a difference in whether or not you will need a center notch, and thus a rafter to notch it to.
Keep in mind, I am not an engineer...I've just dealt with A LOT of purlins!
Good Luck!
*K