In short. I feel that focusing on one language at a time is better if you are pursuing, let's say C1 or C2 in a handful of languages. However, as BeaP said, it depends on circumstances. I don't agree it depends on age, but if age = circumstances/stage in life, then I do agree. Age alone I feel has an impact to a certain degree, but I feel motivation, health and fitness (not just age - one can be a very energetic 70 year old or a very unhealthy or perhaps unwell 20 year old), energy levels and how busy one is can overcome even advanced age where learning is concerned.
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I'm going to provide my opinion based on my experience. If you've heard my story before, skip to my final advice down the bottom of the post (I think I just like waffling about my language learning history, and where better than here to do so, right?).
The first time I started to learn languages on my own with a degree of seriousness and a long-enough goal (9 months to one year), I learned both French and Spanish simultaneously. Interference wasn't an issue. Motivation was good most of the time. Free time was plentiful (although I didn't realise how good I had it!). But I remained naïve even after the 9 or 10 months of study, since I didn't know how much more learning was required to take these languages to an advanced level, and I stopped.
Years passed in which I studied a mixture of absolutely no languages, one language, two at a time, three at a time, four maybe? (I can't remember) - French, Dutch, Spanish and German were the chosen languages (although German was focused on less than the other three over the years). I wanted to learn 7 at once at one point, but even with most of my days completely free, the idea of learning 7 at once led to inaction resulting from stress (at the thought of spending much of my days learning, despite wanting to). So I learned between one and four (usually two or three) at home and later in Europe. in 2011 I learned Dutch solidly and only Dutch in the Netherlands for a good several months. I got close to B2. I was beginning to realise how much work was required to get to an advanced level. I was also developing the ability to study for longer periods of time on a daily basis. I returned to learning three languages at once (NL, ES, FR) in Europe once we left the Netherlands.
Several years back now back in Australia after feeling like I wanted to really get to an advanced level just in one language (French), I stopped studying more than one language at a time, simply because it would give me more time to devote to one. I really didn't think it would take so long. I passed B2 and failed an attempt at C2. Where did I end up? Somewhere in between I guess.
Burn out meant I didn't reach the elusive C2. Wanderlust kicked in and I think I jumped ship to a new language in part because it just took so damn long to start feeling like I was on the cusp of an advanced language user (likely partially my fault for using predominantly inefficient learning methods and not using enough native content) Life started getting in the way more and more, I was exhuasted, I chose another language to learn and decided to come back to French later.
Conclusion? If you have
plenty of time, by all means you can indeed learn more than one language at a time, provided you can handle it. You can also do it, albeit very very slowly if you don't have much time, thus I don't recommend it. Moreover, younger with lots of free time doesn't always equate to the ability to commit to sustained study every day (of several languages). This is I feel where being older (with more experience) trumps being younger (less organised, less study endurance etc).
And yet I returned to using multiple languages in the household. I still only focus on actively learning one language at a time (on my own - currently Norwegian), yet I'm using a few languages at home with the kids. French beame part of the family and as I'd had a decent Dutch learning background (2nd to French), I have been able to introduce it (resurrect it for me) into the faimily environment as the second foreign language. Spanish, since initially learning a good amount all those years ago, has remained a straight-forward language to read, so I do so with the kids here and there. As we language nerds generally agree, introducing kids to languages earlier is beneficial, so I'm focusing on learning Norwegian myself now with an aim to be able to introduce it to the kids as well in the near future. So I focus on one and the others grow together with the family at different rates.
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EDIT:
The multilingual situation I have encouraged with my children is not to the detriment of advancing in the language I am studying intensely on my own (currently Norwegian). I speak and read for example with the kids in FR, NL, ES (read only) but due to the fact that we homeschool, this takes no time away (usually) from dedicated language study on my own (Norwegian intensive study). Thus, I would not classify myself as learning multiple languages at once, strictly speaking, at least not intensely. I would be doing these things (reading, speaking, watching) with the kids in English if it were not in the other languages mentioned. My dedicated intense study time is a separate activity, outside the kids learning time or my interaction with them. Perhaps if we didn't homeschool at all we'd have more time for our own activities, but at least doing so with foreign languages allows for slow learning/maintenance of my other languages for me personally, and facilitates their foreign language growth as well. So, with what little free time I can scrape together (stolen moments, some dedicated study time), there's really only time for one language. Once this language is implemented into the kids routine (initially some reading), I'll be able to return to chosing another language to intensely focus on in my time. That's most likely going to be a language I already use and want to improve, unless of course I'm the type to not take heed of my own advice! Me, never!
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Final advice:
Intensely study one language at a time for as long as you can (to take it to C1/C2 or beyond). Other languages can be used/maintained (or even lightly dabbled in) at the same time if the situation calls for such. If you're young with lots of free time you're likely not keen on intensely studying languages all day anyway. If you're older, you're likely more capable of enduring longer hours of intense study (imo), but don't have the time due to other committments. Thus, one at a time generally fits most circumstances, but not all. If you have lots of free time and motivation to put into language learning, the situation is different and much less common, so do as you please.