We present magnetization and magnetostriction studies of the insulating perovskite LaCoO3 in magnetic fields approaching 100 T. In marked contrast with expectations from single-ion models, the data reveal two distinct first-order spin transitions and well-defined magnetization plateaux. The magnetization at the higher plateau is only about half the saturation value expected for spin-1 Co3+ ions. These findings strongly suggest collective behavior induced by strong interactions between different electronic -- and therefore spin -- configurations of Co3+ ions. We propose a model of these interactions that predicts crystalline spin textures and a cascade of four magnetic phase transitions at high fields, of which the first two account for the experimental data.