It is possible to complete parts of the Master's programme abroad. First you must consider doing a research internship or writing your thesis in another country. Completing course modules abroad is more complicated, since the Master's programme has a set structure that leaves little room for introducing electives.
If you wish to do an internship or write your thesis abroad, you will need to arrange it yourself. You need to start your own search for a place to conduct your research or write your thesis and do so well in advance. You can use the international contacts within the study programme. It is also possible to do a professional internship, but this may cost more effort.