It is necessary to separate the two patterns far enough that overlap is not great, and then you will get the effect of the pattern reforming and creating a much narrow front lobe as shown in figure 4. Its as simple as that. The pattern on the right show the pattern of single beam. When stacking distances are too close, there is not really any effect from stacking, the pattern remains the same as having a single antenna. Figure 4 - The result of stacking beams with a wide enough spacing.
Lets look at some possible physical arrangements for co-phasing.
This is the most common arrangement. A stacking boom must be made to support the two antennas. HERE is the plan for a stacking boom designed by Antenna Specialists. I do not know of anybody that commercially makes a stacking boom. Another possible combination of stacking two antennas is shown in figure 6.