I'll just look at the interesting case of a plate with charge $Q$ facing a neutral plate.

In the plate dimension >> plate separation, uniform field approximation, the charges on the plate surfaces are:

$+Q/2$ on each surface of the charged plate. $±Q/2$ on the surfaces of the neutral plate, with $-Q/2$ on the inner (facing) surface and $+Q/2$ on the outer surface.

Taking account of the charges on all 4 surfaces, and the fields that they give rise to, you'll find that the resultant field inside each plate is zero.