This paper contributes to the conference discussions of (1) “what are the trade-offs and synergies between the economic, environmental and social dimensions of the Common Agricultural Policy (CAP) as a policy geared towards sustainability”; and (2) how to measure the performance of agriculture at a range of scales. Specifically, we assess whether there are tensions for CAP policy between enhancing productivity and the provision of public goods. Our insights are derived from an EU Horizon 2020 project, Moving Towards Adaptive Governance in Complexity: Informing Nexus Security (MAGIC) exploring the robustness of policy narratives in the water, energy, food and environment nexus. As highlighted in the conference objectives, assessing the role of the CAP in delivering sustainability requires taking multiple, non-equivalent perspectives (e.g. geographical scales or structural hierarchies). The conduct of these multi-perspective studies is guided by the concepts of societal metabolism analysis. The analytical focus is thus on understanding the mix of biophysical and socio-economic resources needed to maintain social-ecological systems (e.g. food and farming systems) and the degree to which these are met locally, highlighting where there may be dependencies on other systems or externalised impacts. We conducted transdisciplinary research with policy makers using Quantitative Story Telling (QST). The QST process has a phase of qualitative analysis of the institutional and semantic framings of CAP policy narratives, followed by formal quantification of the robustness of policy narratives using the MuSIASEM toolkit for societal metabolism analysis. Interpretation of these formal analyses, with stakeholders in DG Agri and other EU institutions, closed the loop. The results of this analysis (and of other analyses for Biodiversity, Circular Economy, Energy Efficiency, and Water Framework Directive) are available via the MAGIC document repository. From the semantic qualitative phase, the narrative selected as the basis for formal analysis was: “CAP aims to ensure European agricultural competitiveness in the world market and aims to deliver public goods such as biodiversity conservation, water quality and climate change mitigation. These aims are in opposition”. The formal societal metabolism analysis was pan-EU, focusing on key aspects of EU farming systems. These characterized imports and exports of agricultural commodities, the relative intensities of inputs use in production systems and the aggregate impacts of production systems on environmental indicators. Farm Accountancy Data Network (FADN) data and Eurostat CAP impact metrics already include variables that can support these pan-EU societal metabolism analyses. Adding more bio-physical quantities to those existing within FADN, particularly for inputs and outputs, would enhance its analytical value, particularly for identifying externalisation and pressures on the environment.