Your logbook is your logbook, and doesn't have to be separated according to licenses. It's a record of your total flying experience.
I have the same logbook for my FAA as my JAA. Any particulars to satisfy certain license requirements are easily separated. Like for instance cross country between FAA and JAA: I keep tab of which xcountries are over 50NM to satisfy FAA, but also record for JAA. I even have my (very few) helicopter hours in the same book. I used to have a separate book for helicopter but it didn't make any sense, so I transferred them and made a note about it. It's all flying.