This theoretical work demonstrates that as many as thirty two new shear-horizontal (SH) acoustic waves can propagate in the piezoelectromagnetic transversely isotropic (class 6 mm) plates. These theoretical investigations relate to the homogeneous boundary conditions when the same set of the mechanical, electrical, and magnetic boundary conditions are applied to the upper and lower free surfaces of the piezoelectromagnetic plate. These new dispersive SH-waves propagating in the piezoelectromagnetic plate can have an infinite number of modes when the phase velocity Vph is larger than the speed Vtem of the bulk acoustic SH-wave in the plate. For Vph < Vtem, the new dispersive SH-waves can have the corresponding fundamental (zero-order) modes. It is apparent that knowledge of plate wave properties can be also beneficial to design of smart devices, biological and chemical sensors, filters, resonators, actuators, etc., and useful for the aerospace industry which calls for innovative smart (composite) materials. Also, it can represent an interest in constitution of piezoelectromagnetic laminate (composite) plates in the microwave technology and nondestructive testing and evaluation.