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 the knock-on effect. 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 obtain positive density of reformed nodes on that layer. Full density can only be reached in the absence of risk of reform abrogation. The opposite case 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 thus provide a formalized argument in favor of giving equal weight to all aspects of sustainable development.