Installing app on external drive

Hello! I no longer have access to my old Mac and it turns out the versions of CC apps on iPadOS are lagging behind the desktop versions, so I cannot use my iPad either. I do have access to a different Mac as a guest user, but IT severely limits what can be done on that computer so I can't install anything in it. But, I can plug in an external drive. 

So, is there a way to install Illustrator on this external drive, given the Mac I will be using does not allow writing to the internal SSD?

Thanks!