Hell to the no.
Harry isn't like James Bond or Indiana Jones. He wasn't created to have thrilling but essentially unrelated adventures for as long as the author can come up with something. The Potter novels are one story about Harry's lifelong (at least until the age of 17) epic struggle with the incarnation of Ultimate Evil. It's not wizard of the week episodic stuff. You could do more stories with him like that, but the real story's been told, and anything else would feel feeble and desperate.
It's like we say on the show, a movie should ideally be about the most interesting thing that ever happened to those characters. I loved LOTR, but I'm not interested in a new movie about Sam's tenure as mayor of Hobbiton in the years that followed. There is no amount of thwarted turnip thieving that makes that as worth telling as the time he helped save the world from Sauron.
EDIT: it's also why I've never wanted to see a fourth BACK TO THE FUTURE. In the end, the trilogy is a single story (which, if we're honest, goes to the frontier-town mansion in the third act). The story was all wrapped up in the end. Another film would feel like the odd man out.










