The UN Sustainable Development Goals (SDGs) encompass environmental, social, and economic dimensions which are linked to the characteristics of place and have a strong local dimension. They are interconnected at local scales in complex ways which makes progress difficult to predict. To understand how these interconnections play out at the local scale, we co-designed a systems model of the SDGs with a local community using a specific case study in Australia. In this paper, this multi-component model is fully documented, tested for uncertainty, and we have described a Business-As-Usual projection to illustrate its use. We found that integrating insights from local communities in a model co-design process can elicit far more societal interconnections between the SDGs compared to the current dominant model-building paradigm which typically does not involve meaningful stakeholder involvement. Social issues are often intensely local in origin and effect and attempts to model them at national or global scales may not succeed. Via local scale model co-design, we can tease out the interconnections between societal and non-societal issues and have a greater chance of identifying effective solutions to broader sustainability problems. Our results demonstrate that modelers alone are not fully aware of contextual differences and locally specific interactions that drive the behavior of systems and SDG progress. Stakeholder participation at the local scale is critical for human-focused modelling that better appreciates local nuances. The local SDGs systems model fills a research gap between global, multisectoral, integrated models, and single-sector models applied to local case studies.