The answer is: NO! It can't be done. And no unlike popular believe women are also not able to do this, they only manage better than men to hide it. It is proven the human mind can only fully focus on one thing at the time. This is also precisely the reason why most countries banned using a cell phone while driving.
Now even computers can't multi-task. They still perform all tasks one by one, but as such a high speed that humans can't catch up and so the illusion of multi-task is created. However, you will notice that if you have too many programs open on your computer it will eventually slow down, or put programs on hold that it deems lesser important. Although, a little catch is in order as these days computers have multiple CPUs but that's basically cheating. You can see that as a human with two heads and one head focusing on one task and one other head on another task, and that is not true multi-tasking in its purest meaning.
Scientists have indeed, as TheCartoonMemer pointed out, confirmed that true multitasking is an illusion.
A nice example, I am drinking coffee while writing this... Or am I... No I basically stop my typing whenever I take another sip of my coffee, so basically I put one task on hold in order to be able to perform the other, only to resume the main task when the other is done.