All of the the research I have seen on this topic have been observational retrospective studies, which are worthless and should be ignored. The confounders on the group of people who are able to learn a second language (let alone a third or more) are so large that they cannot be overcome without a randomized control. This stuff is churnalism, right up there with "does coffee make you live longer?" [1].

But, as someone who has now devoted a large portion of my life to becoming proficient at a second language, I do think there are benefits, even if they've never been proven. The most important of these, in my opinion, is just the social aspects of learning another language. You have to get out there and talk to people, and that's inherently healthy.

I do want to say that you hear loads of pessimism about whether or not it's possible a language after childhood, etc., but I'm here to tell you that not only is it possible, it's possible to do even if you suck at languages (as I do). The primary factor is motivation, and the second biggest factor is time. Find a language that you like, because you like the culture you'll be interacting with when you speak it. If you don't, you'll never find the impetus to keep going when it gets hard and boring.

[1] protip: drink coffee if you like it, and don't worry about it. Likewise, learn a language if you like it, not because some dumb article said it would make your neurons fluffier.

And it is only getting easier to learn a language now too. What FINALLY got me over the hump with Spanish was YouTube and discovering resources like Dreaming Spanish (leveled content for comprehensive input that probably exist in most major languages). Content that was fun and at my level.

Mix into that a weekly lesson with italki from your home and you can learn any language at any age.