Does mutual capacitance increase for two positively charged plates when brought close?
Mutual capacitance is independent of the actual charges that may exist.  It is only a function of the geometry of the capacitor and the dielectric constants of the materials involved. In general, for a parallel plate capacitor, the capacitance is inversely proportional to the distance between the plates.  So therefore if the plates are brought closer, the capacitance will increase.  However, the value of this capacitance depends only on the size of the plates and the dielectric properties of the material between the plates.  The value of capacitance is not affected by whatever charges may be present.