Switzerland aims to further reduce nitrogen and phosphorus emissions from agriculture. We explore the potential of three types of food system interventions. National farm gate budget calculations are complemented with additional indicators for efficiency, sufficiency, and circularity in nutrient management. Calculations also include the part of the global food system that produces agricultural products imported to Switzerland. Our results suggest that the potential to reduce nitrogen and phosphorus surplus through a combination of strategies exceeds the anticipated effect of currently prioritized measures. Our work also highlights how the additional indicators and extended system boundaries broaden the assessment and reveal aspects that would be concealed if relying solely on national farm gate budget calculations within Switzerland. Based on a refinement of our preliminary assumptions and estimations, future work could identify the crop and animal production systems that offer most leverage, as well as help define priority strategies and measures.