I'm not sure what the EU license is, but if it's the same as JAA ATPL theoretical exams, then the answer is simple:
You have over 1000 hrs logged on a Multi-crew aircraft, however, that needs to be recognised as a JAA multi crew (for instance, the BE 1900 isn't). The minimum is 500 on the type.
Then you just go to a training provider with a JAA examiner to hand, and in one check ride (skills test) you can get the JAA CPL, ME / IR, and a JAA type rating on that aircraft. There may be training required at the discression of the training provider. You will also need your class 1 medical issued prior to this. To see if that aircraft is approved as multi crew, call a flight school and get them to check in JAA FCL 1.
Again, not sure what the EU license is, new one on me (but I'm not that old to aviation really)
I hope thats of some help to you
IBR