Dimension can only be used with a background images that have the horizontal line, in the same hight as the 3D object, if you want to have a realistic shadow, from the 3D object on the ground or table etc.
It should be possible to offset the Ground Plane, without changing the horizon:
If I move the object under the ground plane, the object disappears. If the object is floating above the ground plane, there is no shadow under the object and the composition will not look realistic.
If you move the ground plane with the horizontal line tool, the perspective is wrong.
Possibility to add more ground planes:
On a background image, let's say you want to place two 3d objects in two different heights, with visible shadows. For example, a 3d model on the floor with a shadow on the floor and one 3D model on a table with shadow on the table.
Is there a solution to this or have I overlooked something?
You can move the ground planes position relative to your view with the Orbit, Hand, and Dolly tools. I usually do most of my camera alignment manually if Match Image isn't right using those three tools.
In regards to having multiple heights (IE shadows on the floor and on a table top), that's not possible yet. There is only the one central ground plane object for catching shadows.