Multi-location studies are increasingly used in environmental epidemiology. Their application is supported by designs and statistical techniques developed in the last decades, which however have known limitations. In this contribution, we propose an improved modelling framework that addresses these issues. Specifically, this flexible framework allows the direct modelling of demographic differences across locations, defining geographical variations linked to multiple vulnerability factors, capturing spatial heterogeneity and predicting risks to new locations, and improving the assessment of uncertainty. We illustrate these new developments in an analysis of temperature-mortality associations in Italian cities, providing fully reproducible R code and data.