Conceptual problem: Physics and pressure?

If a non-porous, incompressible board floats partially submerged in a sealed container of water and the pressure inside the container is increased by a significant amount (say 50 percent) will the board float lower, higher or remain unchanged? I say unchanged because there is no area on the board's surface where liquid can be compressed enough to change the diplacement volume (as with a Cartesian diver), so the atmospheric pressure change is offset exactly by the change in the upward force from the water. If I'm wrong, why so or how so?