We study the (2+1)-dimensional Gross-Neveu model in an external magnetic field. The model, which serves as a toy model for QCD, has been predicted by mean-field studies to exhibit a very rich phase structure in the plane spanned by temperature and chemical potential as the external field is varied. We investigate what remains of this phase structure beyond the mean-field approximation. Our lattice results are consistent with the magnetic catalysis scenario, i.e. an increase of the chiral condensate with the magnetic field, both at finite temperature and chemical potential.