The Sustainable Development Goals (SDGs) and the Paris Agreement are the two transformative agendas, which set the benchmarks for nations to address urgent social, economic and environmental challenges. Aside from setting long-term goals, the pathways followed by nations will involve a series of synergies and trade-offs both between and within these agendas. Since it will not be possible to optimise across the 17 SDGs while simultaneously transitioning to low-carbon societies, it will be necessary to implement policies to address the most critical aspects of the agendas and understand the implications for the other dimensions. Here, we rely on a modelling exercise to analyse the long-term implications of a variety of Paris-compliant mitigation strategies suggested in the recent scientific literature on multiple dimensions of the SDG Agenda. The strategies included rely on technological solutions such as renewable energy deployment or carbon capture and storage, nature-based solutions such as afforestation and behavioural changes in the demand side. Results for a selection of energy-environment SDGs suggest that some mitigation pathways could have negative implications on food and water prices, forest cover and increase pressure on water resources depending on the strategy followed, while renewable energy shares, household energy costs, ambient air pollution and yield impacts could be improved simultaneously while reducing greenhouse gas emissions. Overall, results indicate that promoting changes in the demand side could be beneficial to limit potential trade-offs.