You can launch Notepad++ with the -multiInst Command Line Switches. This will enable launching extra instances when opening files by double click or right click. Any command line will do, including the one that you can access from the Properties of the desktop shortcut.
You can always send a document being edited to another instance from the View menu or the tab right click menu, or call Run -> Open in another instance, regardless of this setting.
To force one file per instance Notepad-like behaviour, see Notepad-like Behaviour. This will hide the tab bar, but you can restore it from Settings -> Preferences -> Tab bar.
You can also access the properties of the Explorer Context Menu, and plug the -multiInst switch in the command line available there.
The Settings -> Preferences -> Multi-Instance preference widget allows choosing between the way Notepad++ handles multiple instances:
- by default, us single instance mode
- always use multiple instances
- open session in new instance