Generally speaking, no, an extraordinary minister may not serve outside of his or her parish. They are appointed for the task of helping the distribution of communion in their own parish only, they do not exercise this function by right.
However, there is one exception. In an emergency case the priest may depute an individual to be an EMHC for a single occasion (GIRM 162). This is a rare exception and the person is appointed only for that one occasion.
