NESTING a clip?

I am a Premiere user. In Premiere I can just NEST about everything. In case you do not know how - here is how it works: I add a bunch of effects to a clip and then I nest the clip so all the effects and what not are inside the nested composition and inside my time line I have a ...virgin clip / vanilla clip (or whatever you want to call it) without any effects on it (the effects are inside the nesting on the clip) so I can add new effects to it.
I hope there are some Premiere users here / people who get what I was just trying to explain. Now here is my question: Is this possible in Avid and IF SO how? It adds a lot of flexibility. I am doing a video mix down on my clips in order to add something else on them if I can not add it with ALT drag yet that's annoying. If I could nest I would not have those problems.