that is a good question, i don't know if multiple contexts can be established in PJSR. i sort of suspect not, but it is hard to know since generally scripts block the UI, preventing you from even trying.
one thing you can do is run an entirely new instance of pixinsight itself:
/Applications/PixInsight/PixInsight.app/Contents/MacOS/PixInsight -n
you can also say --help to see all the command line arguments available. there are a lot of IPC type things and some newer background modes which i think are an offshoot of AstroBin using PI to do all the solving/annotation.
rob