Legendary makeup artist Rick Baker (An American Werewolf in London) was interviewed by British movie magazine Empire, and he mentioned the difficulties they had during filming:

“It was a crazy production. We had a writer actually on the soundstage writing the words moments before the guys had to say them. I don’t think that’s any way to make a movie. [...] But I’ve seen a rough cut and I was actually shocked at how good it was!”

And when he was asked about a further sequel, Baker said:

“At least we’ve got Josh Brolin now to carry on with Tommy’s part…”

I’m guessing that would mean killing of Tommy Lee Jones, and shifting the younger Agent K to yet another period in time, presumably the future? But maybe the future would be too expensive to create? Perhaps get Luc Besson (The Fifth Element) to direct it?