Superimposed phase diffraction grating were formed by an electron beam in amorphous arsenic sulfide (As2S3) films. The number of superimposed gratings was N = 2 - 10 and the misorientation angle was pi/N. The electron-beam-stimulated modulation of the refractive index n1 = = 10(-3)-10(-2) of the superimposed gratings was studied as a function of the number of these gratings. The main factor which limited the number of mutually independent superimposed gratings was the limit of linearity of the response of the recording medium at the nodal regions where the total radiation dose was maximal.