The framework from the first talk will now be applied to polyhedral products. The polyhedral products based on pairs (cone on loop suspension X, loop suspension X) and (suspension X, point) are naturally connected. We show that there are compatible filtrations in which successive layers are controlled by Whitehead products and higher Whitehead products. This arises more as a consequence of the homotopy theory of the suspensions rather than the combinatorics of the associated simplicial complex.