Most large modifiers come with two diffusers. A big one for the outer rim and a smaller one that fits between the source of light and the big diffuser, right in the middle of the modifier. Of course, this begs the question how may diffusion layers do you actually need. Photographer Francisco Joel Hernandez shares a short, yet informative video on how diffusion of strobes effects portraits (or any other type of shoot).
Francisco demonstrates that the tradeoff is pretty simple, the more diffused you are, the less power you get. More diffusion also means less contrast.
Less diffusion runs the risk of more spekular highlights (or “hotspots”) and harsher shadows. Both mean exposing every cress, creek, and pipmle in the skin. Here are samples which make the comparison pretty clear
For the full breakdown head over to Francisco’s video