Suppose we are given a fixed ambient symmetric monoidal model category (I'm mostly interested in chain complexes over char zero fields). Then we have the notion of an $E_n$-operad in that category. Moreover we have a model structure for operads, we can speak about homotopy operads, infinity morphism of operads ect.
In such a setting. Is there any interesting structure on the set of all possible (homotopy) $E_n$-operads?
I know, this question is far from being precise. That's basically because I don't know what I'm after at this point. Therefore anything might be interesting.