A third point can come into play in perspective, but only when dealing with extreme heights or lows.
Tall buildings are one example.
This vanishing point is always directly in front of the viewer at a 90 degree angle to the horizon line. If looking down at an object in three point perspective it is referred to as a bird's eye view. M.C. Escher uses three-point perspective in the piece Ascending and Descending . Even though this is similar to a two-point perspective exterior, he is using the third vanishing point to allow the viewer to perceive the vertical depth. You will notice that all 90 degree angles recede to one of these three vanishing points.