We study the resilience of a multiplex socio-ecological system (SES) which we structure from the spheres composing the sustainability Venn diagram. The SES network is subject to dynamics of spread of a global reform through a knock-on effect, as a direct and indirect repercussion of a small-scale reform process that spreads out over time through network connectivity. The model outcomes reveal that high probability of reform completion on an SES layer through nodes previously reformed on other SES layers is necessary and sufficient to propagate the desired reform on that layer. The maximum asymptotic density of reformed nodes can only be achieved in the absence of risk of reform abrogation. When the risk is significant, it prevents the equilibrium density from reaching a steady state. The numerical simulation results show that the combination of likely probability of reform completion and of proportional influence of all layers yields the maximum magnitude of efficiency of the knock-on effect. We provide a formal argument that favors assigning equal weight to all aspects of sustainable development.