In my previous answer I was assuming the slope was behind and above your building: the answer still could apply to downwards slopes but was not in the intent. By going deeper unto the soil some superficial loss won't affect as much your building.
If your addition comes close to a downwards going slope, you may use some centering beam solution to the foundation of the loads coming close to the edge. Such loads will be passed in cantilever to more inwards footings, and balanced by loads at the other end of the centering beam by part of the building weight placed there. This way you put your foundation load farther frome the edge, and make your building less prone to suffer damaging distortion if the slope is partially washed or shows some superficial instability. It might even loss support there and your building stnd on the centering beams' foundation. You could then simply re-fill.
On the other hand, except that the slope is feared to show slippage, as long it is less than 2 horizontal to 1 vertical it shouldn't give any special problem. The only precaution when one feels sure on the good nature of the stability of the slope is to use a reduced allowable pressure for the foundations.
And one can also analyze the stability of the slope, but normally being gentle it shouldn't show any problem except in extremely poor soils. Try to ascertain if the slope has been stable in all the time of which people remembers, and judge also if it is likely flood or slide conditions can occur. If not, the reduced pressure scheme should work well.
Don't forget in such case to add ties orthogonal to such edge, preferably somewhat stiff, imitating the centering beam action.