[en] Based on the theory developed for the multiple diffraction of neutrons in mosaic crystals, approximate intensity solution have been derived allowing the calculation of multiple diffraction patterns when several (n >= 4 ) beams contribute to the phenomenon. The solutions are appropriate for the calculation of both primary and transmitted beam patterns when high absorption and high secondary extinction are present. A computer program (MULTI) using these solutions has been prepared and applied in a parallel study of the beta-phase of quartz employing neutron multiple diffraction as a method of analysis. In this application, n assumed values which frequently surpassed 20 beams. In spite of the large number of beams participating in the phenomenon, a good agreement between experimental and calculated patterns has been observed. (author)