We theoretically study the Coulomb drag resistivity and plasmon modes behavior for a system composed of two parallel p-type doped GaS monolayers with Mexican-hat valence energy band using the Boltzmann transport theory formalism. We investigate the effect of temperature, T , carrier density, p, and layer separation, d, on the plasmon modes and drag resistivity within the energy-independent scattering time approximation. Our results show that the density dependence of plasmon modes can be approximated by p 0.5 . Also, the calculations suggest a d 0.2 and a d 0.1 dependencies for the acoustic and optical plasmon energies, respectively. Interestingly, we obtain that the behavior of drag resistivity in the double-layer metal monochalcogenides swings between the behavior of a double-quantum well system with parabolic dispersion and that of a double-quantum wire structure with a large carrier density of states. In particular, the transresistivity value reduces exponentially with increasing the distance between layers. Furthermore, the drag resistivity changes as T 2 /p 4 ( T 2.8 /p 4.5 ) at low (intermediate) temperatures. Finally, we compare the drag resistivity as a function of temperature for GaS with other Mexican-hat materials including GaSe and InSe and find that it adopts higher values when the metal monochalcogenide has smaller Mexican-hat height.