It is impossible to have more than one thought at a time.
Try to use your brain to have two unrelated thoughts at the same time. For example think about your kids and listen to a song on the radio - being careful to listen closely and understand all of the words. You can either listen to the words or think about your kids. You may be able to swap back and forth really fast to create the illusion that you are doing both. The two may even get mixed up so that you think about how the words you're listening to relate to your kids. But if you really pay close attention, you'll notice you are either listening to the words or thinking about the kids and never doing both at exactly the same time.
I've asked lots of my friends to try the same thing - none could have two simultaneous thoughts.
So in some ways our minds must function a little like a single-processor computer (up until about 2005 almost all personal computers only had one processing core). Single-processor computers that are sufficiently fast create the illusion of multiple simultaneous computation. Although you can play your itunes and type an email at the same time, the computer is actually going back and forth between the two so fast that you don't notice it. The computer does this swapping by using memory and different buffers. It puts all the information for your email and for your itunes in a short-term memory, and then it simply goes back and forth between the two and computes the next things that need to be computing. Similarly I imagine our brains are just sticking the things we are currently multitasking into a short-term memory, and it just swaps them in and out to think about them. This process creates the illusion of thinking about multiple things simultaneously.
Our inability to have simultaneous thoughts does not preclude us from simultaneously doing multiple things. We must use the spinal cord or other neuronal cells throughout our body as the buffers to keep us running smoothly. So we can think about our next tennis shot while our arm is busy hitting the current one.