In eagle we always did this with third-party plugins, IIRC. I remember running all sorts of scripts to panalize.
I'm currently using whatever the most recent version of KiCad is, and I can duplicate the entire blocks of copper without issue.
The primary feature I have found to be missing is the ability to copy and paste artwork from one file to another. I'm sure it could be done with a plug-in, and I have seen some advertising it.
... If memory serves eagle handles it by systematically renaming everything to make sure there's no duplicates.
... Anyhow, if I understand the question as being related to moving laid copper from one spot to another... I can do that just fine.
-methods