Depending on what changes you’re looking to make, the best option will present itself.
If you’re looking to make design/navigation changes: You should duplicate the theme and work on the one not being used, creating new menus etc if required. Then publish the theme once you’re finished.
If you’re looking to make changes to content (e.g. product content): You’d be better temporarily closing the store whilst you’re making many changes but I’d advise having as much ready to go as possible so you can minimise downtime.
Best of luck!