My current situation is somewhat similar: I started a new job a few months ago, and I'm learning PHP and the Interactive Data Language simultaneously for the job. They're very different in a lot of ways. PHP is pretty similar to other languages I've worked with (C, Perl, etc.), so has come pretty easy. IDL is a bit odd to my way of thinking, so it's going slower. Thus, I'm finding that it can be challenging to learn two languages at once ... especially since I'm in my "extremely late 30's" ;->.
That said, from what you've stated, I assume you're using C# on the job and would be learning JavaScript to use there too. So, you've got plenty of incentive - and presumably time - to learn them and get paid for it. I don't know C#, but have done a fair amount of C and a bit of Java as well as JavaScript, and think they aren't too much different - at least in syntax, so think you'll be fine.
If you're doing this entirely on your own time (and maybe dime), I'd suggest only taking on one other language in a year. It's up to you, but I don't think there would be enough time to devote to learning the languages and living the rest of your life.
Good luck!