I find this very interesting. Most, if not all, of the famous polyglots say that you should do one at a time. However, they also say that we are better equipped than kids to learn languages. I know lots of young kids that speak 5 languages and they learn them altogether. I'm afraid this isn't an answer to your question. I would recommend you to think if there are any personal reasons why you couldn't learn 2 languages at once - time, study methods, other responsibilities etc. and make your mind up that way. I would be very interested in what you decide and how it goes for you. Please keep me informed - if you have the time!

I am currently studying both Korean and Japanese but I'm progressing faster with Korean since I learned the reading and writing much quicker, so I am already studying vocabulary and grammar. For Japanese, after learning hiragana and katakana I started working on Kanji. So far I've only memorized around 650 of the 2,136 jouyou kanji. Like in learning Korean, I wanted to work on my reading and writing in Japanese first but after getting bored of just studying Kanji I decided to study basic grammar as well. It wasn't that difficult to learn Japanese grammar because I'm already familiar with the language being an anime/j-drama fan AND more importantly, there are many similarities between Japanese and Korean grammar. I get confused from time to time though, mixing up Japanese and Korean in one sentence haha. Learning these two languages at the same time is certainly possible, but to minimize the confusion between the two I try to learn them in separate times, like Japanese during the day then Korean at night.

I think it is possible, but it's all about time! If you organise your time wisely you will be able to do it. I personally started learning korean since a year and a half and a few months ago I became interested in japanese too so I decided to learn it. At that time I learnt Kana and some words such as (Hello, how are you) but then I kind of gave up because I found writing rather difficult. Memorizing kanji was the hardest part for me. I have kind of forgot about for a while and started it again (only a week ago) for the 3rd time more seriously.Although it probably depends on the person but it is possible to learn both languages at the same time if you know how to keep them apart! Good luck ^^

I think what you need to do is to make learning each language totally separate. Learn them on different days!