You can change the state of issue. In fact it is required for various reasons - I believe if you become habitually resident or take a flyign job in another state you must change to that state.
However Tigris - what would be unreasonable about a recruitment manager insisting for a job in Europe that a candidate had a significant amount of flight time in Europe? Flying environments are different! Ccertainly I would expect some to show a preference for training in Europe by European instructors.
ICAO is the International Civil Aviation Organisation. It is an umbrella organisation that tries to wome up with international standards. Most nations are members, and their rules comply with ICAO recommendations, or else are published as differences. Their maintenance, training, examining and compliance standards reach or exceed ICAO expectations. The licences they issue in accordance with ICAO are then ICAO licences, and are often recognised internationally (although not always - international law is rather more fickle than national law!). The JAA and FAA licences are ICAO for example, as is, say an Indian one. However the UK CAA NPPL is not.