Many solutions have been defined for multidimensional database modelling. These propositions consider the same aggregation function to determine the values of an indicator according to different levels of granularity into the multidimensional space. We provide a more flexible conceptual model that supports multiple differentiated aggregations. Multiple aggregations allow associating different aggregation functions to the same measure for each dimension and for each hierarchy. Differentiated aggregation allows specific aggregations at each level (parameter). Our model is based on a double graphical formalism, expressive enough to control the validity of aggregation functions. We also study the consequences of this conceptual modelling for building lattices of pre-computed aggregates in a relational online analytical processing (R-OLAP) environment.