Network-agnostic MPC protocols tolerate simultaneously a higher number of corruptions \(t_s < n/2\) when the network is synchronous, and a lower number \(t_a < n/3\) when the network is asynchronous. As such, they provide strong resilience, irrespective of the type of underlying communication network. We focus on improving the communication complexity of network-agnostic MPC with optimal resilience \(2t_s + t_a < n\) . In this regime, there are no polynomial-time information-theoretic solutions and current computational protocols (without fully-homomorphic encryption) communicate \(O(n^2)\) elements per multiplication gate. In this work, we significantly advance the landscape by introducing the first information-theoretic protocol with quadratic communication per multiplication gate and the first computational protocol with linear communication per multiplication gate based solely on signatures and symmetric-key encryption.