It is not allowed to have permanent residence permits from multiple EU countries, for the obvious reason that one can’t be permanently resident in two countries. However, if you are resident in EU country for 5 years, you can apply for a “EU long term residence permit”, which allows you to go to other countries and do other things pretty much as if you were a citizen.
However I think it is possible to have multiple temporary residence permits or visas. The issue is that different residence permits and visas have different requirements and they need to not be in conflict. Since every country has some N different types of permits, all with different rules and requirements, the rules can easily conflict. For example, a D7 requires you to be in Portugal for at least 6 consecutive months, but a German aufenthaltserlaubnis is lost if you are gone for over 6 months, so in practice you can’t hold both unless you can teleport at midnight on the 6 month boundary. A GV has fewer such requirements and thus it may well be possible to hold another permit. It just means a bit of a dance to keep all your permits sorted.
But I don’t know.
If you are using the standard Mercan lawyers, they may not be well-versed in these matters - after all you’d need someone who actually dealt with these kinds of situations - so as someone else said you probably need to ask a lawyer that has experience.