You will run into problems when you train in more than one martial art. The multiple martial arts will clash in your thinking and in your actions, causing indecision. For example, if you train using a karate style side snap kick part of the time and then also train using a Taekwondo side thrust kick, when you spar or have to defend yourself, your brain and body will hesitate for a second before acting to decide on which type of kick to use. This hesitation may be the difference between your living or dying. Also, many martial arts, and their instructors, demand conformity to the art. I once used a karate style side snap kick while sparring in front of a Korean Taekwondo master. After he finished with me, I decided not to use karate style kicks again.
Look at the following chart and try to make yourself say the color of each word aloud, not the word itself.
The right side of your brain tries to make you say the color while the left side of your brain tries to make you say the word. Usually the left side wins and you say the word, no matter how hard you try not to say it.
This same type of mental conflict occurs when you have trained in two opposing ways to fight and you must instinctively react to an attack. In a surprise attack, when your reaction may determine whether you live or die, you must have one instinctive reaction. If you have more than one type of reaction to choose from, will may hesitate and die.
Many martial arts have the premise that, to understand the true meaning of a hyung/kata/form, one must perform it hundreds, if not thousands, of times. If we assume a master of a martial art understands the meaning of all the forms he or she performs, then it can also be assumed that the master has performed each form hundreds or thousands of times. If a person claims to be a master in multiple arts, where did the person find the time for all this training.