Yes, starting in 3.3 you can run multiple instances on one PC. But this feature is not documented, because it is not supported. It is not supported because the application was never designed to run this way. It is possible to lose preference settings, or database changes, when running multiple instances. So I don't recommend it. But if you're willing to live with the possible consequences, be my guest.
In order to run multiple instances, you need to pass the option -tdnoconcurrencycheck to the program at launch. To do this you can modify the shortcut you use to launch the TD application. Right-click the shortcut and select "Properties". On the Shortcut tab, edit Target and add this option. It will probably look like this:
"C:\Program Files (x86)\The Tournament Director 3\TD.exe"
Change it to:
"C:\Program Files (x86)\The Tournament Director 3\TD.exe" -tdnoconcurrencycheck