That is not an uncommon situation, typical with acid, caustic, fertilizer, molasses, sulfur, etc. And normally, the tanks are just hydrotested like normal.
A similar situation occurs when you add corrosion allowance. The hydrotest will stress the as-built shell higher than a light petroleum product will, but likely still won't reach the design stresses due to the extra material.
If the contents were especially hazardous, you could increase RT as Joe suggested. If it was a very small tank, you could actually overfill and/or pressurize the tank. You could add 50% extra shell height as freeboard, and then operate at 2/3 the shell height, but I've not seen this actually done in practice. The problem then is that somebody somewhere is likely to fill the tank up beyond the 2/3 point anyway, so you may be creating a hazard rather than reducing it.