That's one of those urban legends. As far as I know, the origins of ID4 were Emmerich and Devlin talking in an interview about how alien invaders would be more likely to show up in big cities than abducting farm animals, and one of them then said that they'd found their next movie.I read somewhere that Independence Day was originally a sequel to Stargate. With Ra’s race coming to Earth to attack. I don’t know if it’s true though
As for another sequel, not everything has to be a franchise. Sometimes a movie, even a successful one that's still popular years later, can just stand on its own.