It seems to me that cap4000 is talking about the dimension of the pit which is perpendicular to the face of the wall to be underpinned - not to the actual excavated vertical depth.
The depth back from the face of the footing being underpinned can be almost any dimension, even greater than 4', as long as you don't undermine so much of the footing that you cause settlement. I've done pits that were about 6' along the wall face by 8' back under an existing, large, continuous, wall and footing which supported an urban passenger train terminal. Large pits need to be done carefully. This meams proper shoring of the pit sides with extra thickness lagging boards. Usually, normal pits are shored with 2x10 dressed lumber. Larger pits may need rough cut 3" or 4" nominal thickness lumber. Extra consideration must also be given to the corner connections for extra long shoring boards. A few nails may not be sufficient. As long as you don't undermine too much of the footing, shore the sides every four vertical feet (or more frequently if bad ground conditions), and use proper shoring, you should be able to successfully underpin the structure.