We study the generalization of S-duality and Argyres-Seiberg duality for a large class of N = 2 superconformal gauge theories. We identify a family of strongly interacting SCFTs and use them as building blocks for generalized superconformal quiver gauge theories. This setup provides a detailed description of the “very strongly coupled” regions in the moduli space of more familiar gauge theories. As a byproduct, we provide a purely four dimensional construction of N = 2 theories defined by wrapping M5 branes over a Riemann surface.