Yes you can mix different brands but I recommend you do not mix different weights. You can even mix synthetic oil with conventional oil. But as the weight of the oil is critical, do not ever mix one weight of oil with another, no matter if it is synthetic or conventional oil.
Yes, many believe that you can not mix any oil blend together. This is not true, full synthetic can be mixed with conventional also with no harm. If this is done, there is just wasted cash when buying the synthetic.