Are you sure about that Sd?
I always put the shim under the rearmost ring (nearest the eye of the user), this has the effect of tipping the scope downward relative to the bore of the rifle, thus lifting the point of impact within the sight picture.
The OP suggests that he has run out of vertical adjustment, which I take to mean he feels he, or others ‘can’t adjust the crosshairs any higher on the target’, but I may be reading the matter incorrectly?