No, since the election in 2004 it is no longer possible for a Member of the European Parliament to be a member of a national parliament in the same period.

In its original form the European Parliament consisted of an assembly of politicians who were at the same time members of the national parliaments in the Member States, and down the years it has been normal for Members of the European Parliament to have dual mandates. The Parliament’s tasks have gradually developed and become so extensive that it is considered difficult to exercise a dual mandate. With effect from the European Parliament elections in 2004, the Act concerning the election of representatives of the European Parliament by direct universal suffrage was therefore amended so that it no longer is permissible for Members of the European Parliament to be members of a national parliament at the same time. 

Furthermore, Members of the European Parliament cannot be members of a government or of other EU institutions, such as the Commission.