The magnetic phase diagram of magnetoelectric LiCoPO₄ is established using neutron diffraction and magnetometry in fields up to 25.9 T applied along the crystallographic b axis. For fields greater than 11.9 T, the magnetic unit cell triples in size with propagation vector Q = (0,⅓,0). A magnetized elliptic cycloid is formed with spins in the (b,c) plane and the major axis oriented along b. Such a structure allows for the magnetoelectric effect with an electric polarization along c induced by magnetic fields applied along b. Intriguingly, additional ordering vectors Q ≈ (0,¼,0) and Q ≈ (0,½,0) appear for increasing fields in the hysteresis region below the transition field. Traces of this behavior are also observed in the magnetization. A simple model based on a mean-field approach is proposed to explain these additional ordering vectors. In the field interval 20.5-21.0 T, the propagation vector Q = (0,⅓,0) remains but the spins orient differently compared to the cycloid phase. Above 21.0 T and up until saturation, a commensurate magnetic structure exists with a ferromagnetic component along b and an antiferromagnetic component along c.