different languages are like different kinds of sport -- so you can enjoy 1) running, 2) jumping and 3) swimming one by one during the same day :D

Absolutely! If you have the time and motivation, it's perfectly fine to work on more than one language at the same time. I would suggest choosing a language which is very different to Japanese so that you don't get confused, at least at the beginning (I study some languages which are similar to each other, but at different levels). You also need to be disciplined in order to improve in each language. It's a good idea to set aside at least 10 or 15 minutes for each language each day.