If you duplicate a layer or a pre-comp in the timeline you have not changed the source.
If you duplicate a composition in the project panel you have made an independent copy. If the comp has pre-comps then you need to duplicate the pre-comps in the project panel and replace the original pre-comps with the duplicates in your duplicate composition. Now you are free to change anything without effecting the original.
It's critical that you carefully re-name the duplicates to avoid confusion.
You may replace footage in a timeline by selecting the layer in the timeline and then select the replacement footage in the project panel and hold down the Alt/Option key and drag it to the timeline.
There is a script available that automatically duplicates any nested pre-comps in a composition you want to duplicate in the project panel.
I second Rick here - It is critical that you rename your duplicates - not only does it get confusing for you if you dont, I have learned the hard way, that AE can get its expressions confused. Especially, if you have two comps with the same name and similar content. I do work on characters and had the bad habbit of naming the comps "Character_Work being done". I would then import completed AE projects to move effects and collate work done from different departments.) Most of my character layers are stabalized using reverse tracking and I found that sometimes the expressions would link to the wrong comp.
I am now in the habbit of making sure that every layer and every source has a unique name - including those copied or duplictaed. (also, make sure you change the name in the project panel, and not the timeline - the timeline name is for your reference only)