It is demonstrated that the presence of the metal on the walls of dielectric grating slits opens new possibilities for tailoring optical properties of metal–dielectric plasmonic gratings. In particular, a new kind of metal-thickness-sensitive resonances appear due to the excitation of the Fabry–Perot plasmonic modes in the horizontal cavity formed inside the slits by vertical metalized walls. It makes the considered plasmonic structures of great interest for applications where the concentration of the electromagnetic energy is vital. Moreover, transmission peaks related to the Fabry–Perot modes inside the slits etched in the dielectric part exhibit significant enhancement and blueshift as the thickness of the metal on the slit walls increases.