Your languages are probably all cousins
Half the planet speaks a descendant of one unwritten language, and most polyglots never leave the family.
Nobody ever wrote Proto-Indo-European down. It was reconstructed backwards, by comparing its children and working out what the parent must have sounded like. Around half of humanity speaks a descendant.
Which means a European polyglot with six languages has usually learned six variations on one grammar. Cases, gendered nouns, verb endings that mark person: the machinery repeats.
The seventh language is where it gets interesting. Turkish stacks suffixes until one word carries a sentence. Chinese uses pitch where Indo-European uses endings. Finnish has fifteen cases and is not related to any of its neighbours.
Nothing about learning six related languages prepares you for the seventh. That is not a discouragement. It is the reason the seventh is worth more than the sixth.