The EU regulations specify that an individual may only hold one EASA Part-MED Medical Certificate, and that all of the EASA licences held by an individual must be issued by the same State that holds the medical records for that individual.
If you have JAA licences issued by more than one country you must decide which of those countries is going to be your State of Licence Issue for EASA licences - it must be the State that holds your medical records. You will need to do this before the first occasion when one of your licences will go through a transaction with the National Authority that issued it. You must then apply to your single State of Licence Issue to transfer to them any JAA licences you hold that were issued by other countries.
If you have national licences that will only be used to fly non-EASA aircraft, those licences can continue to be used, subject to continuing support and administration being provided by the issuing authorities.