Structural hierarchy is known to enhance the performance of many of Nature's materials. In this work, we apply the idea of hierarchical structure to topologically interlocked assemblies, obtained from measurements under point loading, undertaken on identical discrete block ensembles with matching non-planar surfaces. It was demonstrated that imposing a hierarchical structure adds to the load bearing capacity of topological interlocking assemblies. The deformation mechanics of these structures was also examined numerically by finite element analysis. Multiple mechanisms of surface contact, such as slip and tilt of the building blocks, were hypothesised to control the mechanical response of topological interlocking assemblies studied. This was confirmed using as a model a newly designed interlocking block, where slip was suppressed, which produced a gain in peak loading. Our study highlights the possibility of tailoring the mechanical response of topological interlocking assemblies using geometrical features of both the element geometry and the contact surface profile.