President of the European Council
Although the President of the European Council may not hold a national office, such as a Prime Minister of a member state, there is no such restraint on European offices. For example, the president may be an MEP, or more significantly the Commission president (who already sits in the European Council). This would allow the European Council to concurrently appoint one person to the roles and powers of both President of the European Council and President of the European Commission, thus creating a single presidential position for the Union as a whole.