High field magnetization measurements in pulsed fields up to 65 T have been performed on FePS₃, which is nominally a good example of a two-dimensional Ising-like antiferromagnet on a honeycomb lattice. Measurements with the field parallel to the moment direction confirm the presence of two first-order transitions above 35 T, to M/M_sat = 1/2 and M/M_sat = 1, respectively, at 4 K. The measurements are in contradiction with published estimates for the magnetic exchange parameters, but the contradiction can be resolved by allowing for anisotropic exchange parameters in the Hamiltonian. The magnetization with the field perpendicular to the moment direction is anisotropic, with no transitions observed for fields along the a axis while a cascade of first-order transitions is observed for fields above 50 T along the b axis, the latter case also showing a strong degradation of the sample after repeated pulses. The results indicate a strong magnetolattice coupling in FePS₃. Temperature-dependent measurements hint at a possible tricritical point.