Webstorm can be launched from the command line using the command wstorm. However, would it be possible to launch more than one instance? Usually, the second time I run wstorm, it doesn't open another Webstorm for me and does nothing.
If the project has been opened before then you can do: Go to File. Open Recent. Select New Window.
In OS X, this is apparently caused by an outdated wstorm (a Python script at /usr/local/bin/wstorm). I verified the solution indicated in this ticket with WebStorm 2016.1.3:
Go to Tools > Create Command-line Launcher....

UPDATE Nov-2016: As of WebStorm 2016.3, the default name of the launcher changed from wstorm to webstorm. If you prefer wstorm instead, make sure to edit the script name before clicking OK:

Just run:
WebStorm.exe "Full\path\to\the\project\that\contains\the\.idea\folder\of\your\project"
The project will run in the same instance but in a separted window as described here: https://www.jetbrains.com/webstorm/help/opening-multiple-projects.html
NOTE: This was tested on WebStorm 9.0.3 and may not work on previous versions.
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