When you duplicate a layer in the time line it’s still the same nested comp no matter where it is in the time line. Best way is to duplicate it in the time line, then right click and go to source in the project, duplicate the source there and then replace the second one in the time line with the duplicate from the project window. You can do this by highlighting the layer in the time line and option (mac) alt (PC) dragging the one from the project window on top of the second layer in the time line. It will replace it with the new one, with all parameters of the layer that live in the current time line intact. So if you altered the transparency of layer 1 but not layer 2 replacing layer 1 this way keeps the transparency animation intact even though the source is now technically different.
Now you can dive into that new duplicate comp and make changes and it will only effect the second version in the time line.