Comprehensive data analysis has become indispensable in a variety of domains. OLAP (On-Line Analytical Processing) systems tend to perform poorly or even fail when applied to complex data scenarios. The restriction of the underlying multidimensional data model to admit only homogeneous and balanced dimension hierarchies is too rigid for many real-world applications and, therefore, has to be overcome in order to provide adequate OLAP support. We present a framework for classifying and modeling complex multidimensional data, with the major effort at the conceptual level as to transform irregular hierarchies to make them navigable in a uniform manner. The properties of various hierarchy types are formalized and a two-phase normalization approach is proposed: heterogeneous dimensions are reshaped into a set of wellbehaved homogeneous subdimensions, followed by the enforcement of summarizability in each dimension’s data hierarchy. Mapping the data to a visual data browser relies solely on metadata, which captures the properties of facts, dimensions, and relationships within the dimensions. The navigation is schema-based, that is, users interact with dimensional levels with on-demand data display. The power of our approach is exemplified using a real-world study from the domain of academic administration.