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As a continuation of our previously published work, the dynamic phase transitions are studied further, within a mean-field approach, in the kinetic Blume-Emery-Griffiths model in the presence of a time varying (sinusoidal) magnetic field by using the Glauber-type stochastic dynamics. The dynamic phase transitions are obtained and the phase diagrams are constructed in two different planes, namely in the reduced temperature (T ) and biquadratic interaction (k) plane and found eight fundamental types of phase diagrams for various values of reduced crystal-field interaction (d ) and magnetic field amplitude (h), and in the (T, d ) plane and obtained six distinct topologies for different values of k and h. Phase diagrams exhibit one or two dynamic tricritical points and a dynamic double critical end point, dynamic triple and quadruple points, and besides disordered and ordered phases, three coexistence phase regions exist in which occurring of these strongly depend on the values of d, k and h.