Can the body multi-task? Short answer: yes. Slightly longer answer: yes, but with practice. The following activities demonstrate "Bimanual Interference", in which the brain must simultaneously control multiple movements. How many can you do?
1. Draw a circle with one hand, and another circle in the opposite direction with the other hand. Now do both at the same time.
This is actually the easiest. Although, when doubling up, even the most "bi-coordinated" person with need to take a fraction of a second to assess the correct direction.
2. Rub your belly and pat your head. Now swap arms.
This inevitably results in a chaotic rub head, pat belly, rub head and belly, pat belly and head combo.
3. Make a clockwise circle with your right foot, while drawing a "6" with your right hand.
Did the 6 flip around? This can be done quite easily using opposite hands and feet, because you're using two different sides of your brain.
4. Stick a thumb up, and point at it. Now try switching hands.
Achievable with practice, and hand cramp.
5. Rotate your head one way, and your tongue the other way.
Maybe don't try this one in public.