Allow multiple open files
Don't know if that is possible: on Mac OS the OmniOutliner allows multiple open files. OO remembers on exit which files were open and reopens them when starting.
Multiple open files is already possible. I can just double-click on two separate files, and they open in separate windows. The only new thing in this suggestion is making the menu item File > Exit UV Outliner close all windows instead of just the current one and then opening all those windows when UV Outliner starts again.