We consider arbitrarily many interconnected integral Input-to-State Stable (iISS) systems in an arbitrary interconnection topology. We show that global asymptotic stability of the origin of a lower dimensional system termed the comparison system, which is based on the individual dissipative Lyapunov iISS inequalities, implies the existence of an iISS Lyapunov function of the composite system. A sufficient (but not necessary) condition for the iISS of the interconnection turns out to be the generalized small-gain condition derived by Dashkovskiy et al., but this time in a dissipative Lyapunov setting. We also provide some geometric intuition behind growth rate conditions for the stability of cascaded iISS systems.