Volume is an independent variable that can be used to overcome the body's acclimatization to training stimulus. This is particularly useful when the exercise is done for high reps, such as with simple bodyweight work like chin-ups, pull-ups, push-ups, and dips. (More complex bodyweight work would mean gymnastic variations to increase the difficulty of the move, usually through disadvantageous leverage.)
For example, I've found that pull-ups of 15/14/12 would stop doing anything. Increasing volume through extra sets, e.g. 15/14/12/8/8/8 or 12/12/12/10/10/10/8/5 or 1/2/3/4/5/6/7/8/9/10/9/8/7/6/5/4/3/2/1, helped build muscle.