Can the capacitance of a proximity sensor be increase by adding layer to the capacitor?

Unfortunately, this won't work. In order to increase the sensitivity, you'd have to increase the area of near contact between the capacitor plate and your hand. Since all the plates you've drawn are connected to the same node, there's no electric field between them...only between the top plate and the finger. Reducing the thickness of the insulator would proportionally increase the capacitance.