This paper addresses the important question of how national research systems can support the implementation of the United Nations 17 sustainable development goals (SDGs) set out in the 2030 agenda. Much attention on this topic has so far coalesced around understanding and measuring possible synergies and trade-offs that emerge in the SDGs. We contribute to this discussion by arguing that it is necessary to move from a focus on system interaction towards system transformation. A conceptual approach is presented based on the notion that research that “builds bridges” between science and technology and the social and environmental pillars of sustainable development can more fully support simultaneous achievement of the SDGs and thus be transformational. This proposition is put to the test empirically through a study of the Mexican research system using methods from bibliometrics and social network analysis. Our results can help to provide a diagnostic of how research systems are approaching SDGs and where potential exists for transformative research.