Expanding a legal non-conforming unit in Chicago

[Jack Smith]

I run into this problem often in Chicago. A three flat building also has a full unfinished basement or a bit of attic space as well. I would like to duplex down the first floor unit into the basement, or duplex the third floor unit up into the attic. The basement is below grade; so it would not count against my floor area ratio. That would leave me with some square feet of usable space in the attic. The building is zoned RT-4 in Chicago, and as far as I can tell, there is a minimum requirement of 1000 square feet per dwelling unit. The problem is that the lot is only 2500 square feet. Therefore, at least one of the units in the building is non-conforming according to the current zoning. The building is well over a hundred years old, and all three units are legal. But, can I expand a legal non-conforming use unit? Even if I am not going over the floor area ratio for the lot, does the fact that the lot itself is not large enough to support the density of a third unit prevent me from making use of the additional space? I can't seem to find any applicable literature, beyond the building code saying that you cannot expand non-conforming units. Any help would be appreciated. Thanks!