We numerically investigate the formation of stable clusters of overlapping particles in certain systems interacting via purely repulsive, bounded pair potentials. In close vicinity of a first-order phase transition between a disordered and an ordered structure, clusters are encountered already in the fluid phase which then freeze into crystals with multiply occupied lattice sites. These hyper-crystals are characterized by a number of remarkable features that are in clear contradiction to our experience with harshly repulsive systems: upon compression, the lattice constant remains invariant, leading to a concomitant linear growth in the cluster population with density; further, the freezing and melting lines are to high accuracy linear in the density-temperature plane, and the conventional indicator that announces freezing, that is, the Hansen-Verlet value of the first peak of the structure factor, attains for these soft systems much higher values than for their hard-matter counterparts. Our investigations are based on the generalized exponential model of index 4 (i.e., Phi(r) similar to exp[-(r/sigma)(4)]). The properties of the phases involved are calculated via liquid state theory and classical density functional theory. Monte Carlo simulations for selected states confirm the theoretical results for the structural and thermodynamic properties of the system. These numerical data, in turn, fully corroborate an approximate theoretical framework that was recently put forward to explain the clustering phenomenon for systems of this kind.