Ok here is a simple profile of a house, gable end.
Here, just adding a couple of feet of knee wall on top of the top plate of the first floor, one not only adds headroom for a true living space, but by extending the roofline one can add floor space while still keeping the ceiling at the normal height on the first floor. Also, just by changing the angle of the roofline slightly, one can extend the first floor even farther. Of course, this extension of the roofline, means that the roof joists need to be supported by the back knee wall, and the angle of the roof should not be leveled off too much, or snow loads would be far more likely to accumulate. This is especially to be avoided in the north or in heavy snow areas of the country.