Modelling human mobility is crucial in several areas, from urban planning to epidemic modeling, traffic forecasting, and what-if analysis. On the one hand, existing models focus mainly on reproducing the spatial and temporal dimensions of human mobility, while the social aspect, though it influences human movements significantly, is often neglected. On the other hand, those models that capture some social aspects of human mobility have trivial and unrealistic spatial and temporal mechanisms. In this paper, we propose STS-EPR, a modeling framework that embeds mechanisms to capture the spatial, temporal, and social aspects together. Our experiments show that STS-EPR outperforms existing spatial-temporal or social models on a set of standard mobility metrics and that it can be used with a limited amount of information without any significant loss of realism. STS-EPR, which is open-source and tested on open data, is a step towards the design of mechanistic models that can capture all the aspects of human mobility in a comprehensive way.