indigo - you're right that any system of perspective can support a literally infinite number of subordinate points and lines, but this is merely clutter and not an advancement in perspectival systems. These points and guides exist WITHIN in system, and do not DEFINE the system in the way that the chief dimensions do. These additional points represent angles defined rather by a changing x,y,z dimension, they are wholly dependent, do not add anything that cannot be found in the other 3, and so on.
the fact that that object has eight sides which recede from whatever point it is seen from is completely irrelevant to the discussion of perspectival systems, does not even represent the presence of a perspectival system, 8-point or otherwise (there actually are none present in your example, unless you count each frame - the object could easily exist in any perspectival system, or none at all, because it is not spatially defining, merely an object that is dependent upon the system within which it resides) and it's very important to recognize this for a fact.