I'm not sure this would work. The pixels of the sensor are capturing a whole square of incoming light, not just at a single point. Moving the camera 1/3 of a pixel over would just cause 1/3 of the light to bleed over to the next pixel, but it wouldn't increase the achieved resolution.

Oh, wait, maybe this could work. There might be a neat way to take the old and new values of new values and calculate what the in-between area's color must have been, based on how much the bigger blocks changed with a small movement? Either way, you'd need to be pretty far from the subject, but it might work for a landscape?