The magnification does increase with lenses which unit focus-i.e., move the whole lens forward to focus at close distances.
Let's say you put a 50mm lens set at infinity and its smallest aperture on a 35mm camera, and close the aperture with DoF preview, then turn the focus ring to the closest focusing distance. You will see the image get slightly bigger and slightly cropped (and of course, not as sharp). The reason is that as the lens is moved toward the close focusing position, the distance to the image plane increases, effectively resulting in a longer focal length.