Notice that the pattern is unidirectional, and somewhat wider in the plane perpendicular to the elements. This is true in general for Yagis, regardless of the number of directors used. However, as more directors are added, the forward gain will increase, and the beam width will become narrower in both planes.
You may wonder what would happen if additional reflectors are added. The answer is that nothing happens. The first reflector reduces the power radiated rearward to approximately 1% of the forward value. The additional directors cannot couple strongly to the driver because the radiated field passing by them is so small. Only 1 reflector is necessary to reduce rearward radiation.