I will answer with respect to Sweden; as far as I know it can be technically possible but in practice, not really...
Let's expand on this a bit; again, AFAIK, it is not possible to be enrolled to two different masters programs in the same faculty. At least it was not possible when I was in the uni. They might have programs that overlap between different programs and allow you to have a broader portfolio/CV if that is what you desire, but you still get a single degree.
You could try and apply to two different programs at different faculties of the same university. This may work, I am not sure if there is a national regulation on that. I would guess that it's handled by individual university administrations.
The last option is of course applying to two different programs at two different universities, so different legal entities. You could try to get into University of Gothenburg and Chalmers for two different programs for example. I cannot imagine why that would not be allowed.
That being said, if you choose to pursue this, you will very likely have crashes on your schedule such that you will not be able to follow the lectures, and potentially miss some compulsory moments of these degrees. Universities typically don't assume the students do more than 100% studies so you will almost certainly have serious incompatibilities on your schedule.
If you are seriously considering getting two masters degrees in one go (and I would advise against it), my suggestion would be to offset them with 1 year, so that you start one program and half way into that start another. The motivation behind this is that Masters programs often tend to have lecture-heavy courses first, and project or assignment based courses later.