International audience Dealing with contextualized data is a key challenge in data warehouses ($DW$). Nowadays, $DW$ systems are often monocontext. However, in real life applications, $DW$ indicators are shared by many users with different profiles. In this paper, we propose an ontology-based approach for designing multi-contextual $DW$. An ontology formalism incorporating the contextualization concepts is given. We propose to consider the contextualization at the conceptual level. We validate our proposal using a real case study from the medical domain.