Uncorrected Fixed Pattern Noise ("FPN") (right side) will dominate the S/N ratio of an image once a certain signal level is reached (1/PRNU^2) electrons. Irrespective of additional exposure the FPN limited signal will not see any improvement in S/N once FPN dominates. By applying a proper flat field the resulting image will be shot noise limited (left), which is the best you can possibly do. The image above is a simulation.
crop of center region from a flat showing the fixed pattern noise of the sensor (vertical bars)