Unfortunately as far as I am aware you cant do that directly as you cant have two maps open at once and you cant copy to the clipboard while you open another map to paste into as Closing a map would remove the contents from the clipboard. It would a very useful feature if you coul do this though - very helpful indeed would it be.
Currently the best and only real option is to save a number of copies of a map with different names and open each one deleting from each some parts or other of your level - thus splitting it over more than one level.
Always keep a backup of your complete level as a master that you can revert to if something goes wrong.
Hope thats helps