Is it simply like learning two different languages at the same time? If so will it be easier to differentiate if the two styles are very different? For example, Kyokushin Karate and Judo.
It generally takes two/three classes per week (so four/six hours?) to progress in a martial art. Doing two arts, you will need that in both. Three arts brings you to around fifteen hours! That is a lot to fit in a normal day with work and social activities around it. In addition, unless you are really fit, your body will not cope with the strain of that amount of exercise.
Mental space is a little different but the more similar the arts, the more confusion will creep in. So, you might spend time being confused.
I would pick on, get to first dan (or whatever "I know the basics" is in that art) before picking a new one. Although, the more arts you "know" does not make you good at any of them:
I fear not the man who has practised 10,000 kicks once, but I fear the man who has practised one kick 10,000 times. -- Bruce Lee
It's a big commitment to put sufficient time and effort into just one martial art to really get good and advance quickly. Most people who start a single martial art only stick to it for a few months. Biting off more than you can chew is probably not a recipe for success. Training in two martial arts is twice the effort, and if both are intense high-contact styles (as both Judo and Kyokushin are), that may be a cheque your body isn't prepared to cash. (You did say "starting"... it's a somewhat different story to already be proficient in one art and add another that complements it.)
If the reason you are contemplating this is that you are after particular aspects of both, it may be wise to consider finding a single martial art that combines whatever aspects you like about the two you are considering. One example (but not the only one) is Hapkido, which very roughly speaking combines the strikes and kicks of Karate/Taekwondo with the throws and falls of Judo, and also a lot of joint locks, escapes from holds, etc. Sometimes you can also find schools that combine Jiujitsu and boxing, if what you're after is to get skills in both grappling and striking.