Piggyback CPL?

[Golf--Lima--Papa]

I've tried to search for the answer of my question but I had no joy.

I currently have a FAA PPL issued on the strength of my JAA PPL, the FAA one is only valid when accompanied with the JAA one, otherwise known as a 'piggyback PPL'

Now, when I upgrade my JAA PPL to a CPL what happens?

Do I have to apply for another piggyback this time being a CPL piggyback?

In reality I dont need a FAA CPL as the only flying I will be doing while in the states is leisure flying in a single engine a/c, but I'm under the impression when I get a JAA CPL my FAA PPL will then become invalid.

Thanks in advance for any replies.