This paper studies the problem of designing multiagent networks that simultaneously achieve strong structural controllability (SSC) and maximal robustness. Though crucial for effective operation, these two properties can conflict in multiagent systems. We present novel methods to construct network graphs that balance these competing requirements while accounting for network parameters such as the total number of agents $N$ and the number of leaders $N_{L}$ (agents utilized to inject external inputs into the network). We further extend our framework to incorporate the network diameter $D$, thereby generating both maximally robust and strong structurally controllable networks for given parameters $N$, $N_{L}$, and $D$. To assess controllability, we employ the notion of zero forcing sets in graphs and rigorously evaluate the robustness of our designs. We also present a distributed approach to constructing these networks, leveraging graph grammars. This work explores the trade-off between network controllability and robustness to achieve multiple design objectives in multiagent systems.