Stability of the free surface of thin sheets of a metallic liquid on a vertically vibrating hot plate, in the presence of a uniform and small rigid body rotation about the vertical axis, is investigated. The inhomogeneity in the surface tension due to a uniform thermal gradient across the liquid sheet prefers subharmonic response, while the rigid body rotation prefers harmonic response at the fluid surface. The competition results in Marangoni and Coriolis forces acting as fine-tuning parameters in the selection of wave numbers corresponding to different instability tongues for subharmonic and harmonic responses of the fluid surface. Solutions corresponding to various pairs of tongues may be induced in a thin layer of metallic liquid at the onset of parametrically forced surface waves. These give rise to multicritical points involving standing waves of two or more different wave numbers. Bicritical points may involve both the solutions oscillating subharmonically, harmonically, or one oscillating subharmonically and the other harmonically with respect to the vertical forcing frequency. Two tricritical points involving different types of solutions are also possible in a thin layer of mercury. The effect of variation of the Galileo number on critical acceleration and wave number in very low Prandtl number liquids is also presented.