The widespread use of computational simulation in science and engineering provides challenging research opportunities. Multiple independent variables are considered and large and complex data are computed, especially in the case of multi-run simulation. Classical visualization techniques deal well with 2D or 3D data and also with time-dependent data. Additional independent dimensions, however, provide interesting new challenges. We present an advanced visual analysis approach that enables a thorough investigation of families of data surfaces, i.e., datasets, with respect to pairs of independent dimensions. While it is almost trivial to visualize one such data surface, the visual exploration and analysis of many such data surfaces is a grand challenge, stressing the users' perception and cognition. We propose an approach that integrates projections and aggregations of the data surfaces at different levels (one scalar aggregate per surface, a 1D profile per surface, or the surface as such). We demonstrate the necessity for a flexible visual analysis system that integrates many different (linked) views for making sense of this highly complex data. To demonstrate its usefulness, we exemplify our approach in the context of a meteorological multi-run simulation data case and in the context of the engineering domain, where our collaborators are working with the simulation of elastohydrodynamic (EHD) lubrication bearing in the automotive industry.