If you say "run a vi", I assume that you have the VI open in LabVIEW, then press the run button. (Some of the earlier answers taks about programmatically calling VIs, which I don't think is the focus of your question)
You can run as many VIs as you want at the same time. Simply press the run button of the second VI and they will both run.
Of course you should ensure that they don't use the same resources (e.g. DAQ device, or listen on the same TCP port, etc.) In these cases, the second VI might fail. (Also if the second VI is a subVI of the first VI, you won't be able to run it seperately, because it will be already running.)