What you can do is change the plane of focus, to the point where you might even be able to get everything you want into focus. Assuming you can find a plane that everything is on, and can adjust all of the tilts and swings to get that plane in focus.
Originally Posted by gongman5000
The comment about decreasing DOF applies to distance from the camera, because the depth is a spread around the plane which is acceptably in focus and that focal plane is no longer parallel to the film plane, you effectively make it shallower.
I actually think that you understand this, but I figured I'd confirm your thoughts.