[en] We have experimentally investigated the interactions between floating magnetic spheres which are submitted to a vertical magnetic field, ensuring a tunable repulsion, while capillary forces induce attraction. We emphasize the complex arrangements of floating bodies. The equilibrium distance between particles exhibits hysteresis when the applied magnetic field is modified. Irreversible processes are evidenced. Symmetry breaking is also found for three identical floating bodies when the strength of the magnetic repulsion is tuned. We propose a Dejarguin-Landau-Verwey-Overbeek (DLVO)–like potential, i.e., an interaction potential with a primary and a secondary minimum, capturing the main physical features of the magnetocapillary interaction, which is relevant for self-assembly.