The multicritical behaviour of the spin-3/2 Blume-Emery-Griffiths model with bilinear and biquadratic exchange interactions and single-ion crystal field is studied on the Bethe lattice by introducing two-sublattices A and B within the exact recursion equations. Exact expressions for the free energy, the Curie or second-order phase transition temperatures, as well as for the magnetization and quadrupolar moment order parameters are obtained. The general procedure of investigation of critical properties is discussed and phase diagrams are obtained, in particular, for negative biquadratic couplings. The phase diagrams of the model exhibits a rich variety of behaviours. Results are compared with other approximate methods. (C) 2002 Elsevier Science B.V. All rights reserved.