We present magnetization and magnetostriction studies of LaCoO3 in magnetic fields approaching 100 T. In contrast with expectations from single-ion models, the data reveal two distinct first-order transitions and well-defined magnetization plateaus. 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 interactions between different electronic configurations of Co3+ ions. We propose a model 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.