This paper introduces a major new cross-disciplinary research project that looks at the UK health and social care system, as part of an ambitious, broader initiative to apply methods from complexity science to a range of key global challenges. This particular project aims to develop new, integrated models for the supply and demand of both health and social care, in the context of the societal change brought about by migration, mobility and the ageing population. We discuss the background to the work, and the broad way in which we intend to leverage complexity science. This is made more specific with a brief discussion on existing demographic models, and some examples of model-building in progress. We conclude with a glimpse into the subtly difficult problems of fostering such innovative interdisciplinarity.