On PixInsight >= 1.8.6, you can run multiple instances in a much easier way using JavaScript. For example, to run a new application instance, enter this command in Process Console:
j CoreApplication.launchInstance()
You can run up to 255 instances concurrently on the same local machine. This works the same way on all platforms.
You can also run a specific instance by passing an integer parameter from 1 to 256; for example:
j CoreApplication.launchInstance( 42 )
Bear in mind that each instance keeps its own set of application settings in a completely independent way. That is, each instance is completely different in terms of preferences, etc.
You can also know if a particular instance is running:
j CoreApplication.isInstanceRunning( 2 )
Alternatively, on platforms where a terminal is available, you can launch multiple instances from the command line. For example, on FreeBSD and Linux:
$ PixInsight -n
On macOS:
$ /Applications/PixInsight/PixInsight.app/Contents/MacOS/PixInsight -n=2
On macOS you have to specify the instance number for technical reasons beyond scope here.