Moving shapes along different planes on the Perspective Grid

Hi, i am working with a fixed perspective grid that I have set myself.

I'm trying to figure out if there's a way to move shapes with perspective along a different plane?

When drawing a square for example attached to a perspetive plane it can be moved and still retain it's perspective using the Perspective Selection Tool- however this tool only allows the shape to move either up or down within the perspective grid (X or Y) im wondering if there's a way to select it to move along the Z axis- either further back into the image or closer to the front.

I cannot alter my perspective grid as the whole piece is build around a fixed perspective with selected vantage points so I can't attach the plane to the shape and move it that way or id have to go back and reset my grid after. Any help appreciated.