I dont think 3 way will work. The p67 only has 16 pipelines. If you run sli it splits them to 8x and 8x. If you run 3 cards you get 8x 4x and 4x. The GTX670 will easily saturate a 4x connection, it may even saturate a 8x. Chances are if you run 2 670s on that board it will be slower than just running one. 3 will defenitly run slower if it even works.
check out this note, its the bottom line in the specs from the asus site you linked.
*1: The PCIe x16_3 slot shares bandwith with the PCIe x1_1 slot, PCIe x1_2 slot, ESATA3G & PESATA3G and USB3_34. The PCIe x16_3 runs at x1 mode by default for system resource optimization. (PCIe x1_2 will be disabled.)
I have a feeling a video card wont even work in the 3rd slot.