Move/copy parallel allows a distance to be specified (in the x,y plane). We spend a lot of time using this tool, however, we also need to change the elevation. An option to do this incorporated into the tool would save a lot of time using other methods to change the elevation.
While using the Move Parallel tool and AccuDraw, you can rotate the AccuDraw compass to offset and move the element to the "Z increment" elevation, depending on the plane the element is set to move in.