The usual phase-controlled two-beam coupling with heavily doped LiNbO3 crystals leads to the generation of periodic states, characterized by unitary diffraction efficiencies and strong phase oscillations. The maximum refractive index modulation that can be achieved is, therefore, limited by the properties of the feedback system rather than by the crystal parameters. This work presents a method for crossing over the regions of periodic states in order to record photorefractive gratings with saturated refractive index modulations. The method uses the optical anisotropy of LiNbO3 crystals to write both ordinary and extraordinary gratings. Each grating is associated with one eigenmode that can be read out separately by using simple polarizing optics. Because the refractive index modulations for the two eigenmodes depend on different electro-optic coefficients, the unitary diffraction efficiencies are not reached simultaneously for both gratings. This allows for switching the grating used to control the feedback loop so as to cross over the regions of periodic states and to continue the holographic recording process. The method is illustrated for a copper-doped LiNbO3 sample and the values of the saturated refractive index modulations are computed.Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)