The multi-faceted emergencies of our time (recession, pandemics, and international conflict) can disrupt progress towards sustainable development goals (SDGs). While climate-economy models can show pathways out of these disruptions, numerous stakeholder-informed enhancements are required to navigate through the interconnected SDG landscape. We introduce a novel Fuzzy Cognitive Maps (FCMs) approach that integrates Monte Carlo simulations, aiming to capture and understand the differences among modellers' and experts' perceptions of the impacts of such crises on broader sustainability, considering models’ existing/planned capacity and uncertainty over perceived magnitude and propagation of impacts across SDGs. Our application shows that expert stakeholders appeared more concerned over the implications of these crises for sustainable development than modellers, but expectations were considerably constrained by model capabilities. SDGs 8 (growth), 7 (energy-sector sustainability), and 13 (climate action) were robustly found as most prone to examined shocks. Our proposed Monte Carlo Fuzzy Cognitive Mapping (MCFCM) approach also highlighted potentially important propagation effects as well as gaps in integrated assessment model capabilities to holistically study the SDG spectrum.