I speak three languages fluently and a bunch of others to varying degree. I also hold a PhD in Physics. What I've noticed is that my brain manages very well if I have prolonged periods of intense "sciencing" and it also works well if I take some time to learn languages.
However, if I try to do half a day of thinking about algorithms and then half a day of language learning, I will get a headache and slight nausea! Might be that this only happens to me because of some "manufacturing error", but I've tried it repeatedly and it invariably happens.
This has lead me to form the following, highly unproven, high-level working heuristic about the brain: The brain might be just like the rest of our body. You can train to be a weightlifter, or you can train to be a marathon runner. If you do both over the course of your life, you can become good at both, but you'll probably never become the worlds best at any of the two.
If you do intense training on both without a resting period in between, you'll hurt yourself.
So that's my weird theory, for what it's worth.
That said, I think your child has a lot to gain from the broad knowledge he receives. I can tell you from experience that this is the age of interdisciplinarity, and it's a lot of fun.