As the title says, is this possible according to EASA?
According to the Swedish authorities, EASA do not allow attaining a second license before completing the first. But I have a hard time finding anything about it in any document. Their reasoning is that while training for the second license it may interfere and cause confusion with the first one. I do not know how that is possible since you literally undergo the same training as PPL during the basics of MPL/CPL. Getting a PPL sounds more like a complementary thing than an interference.