According to this link I found while doing some Twitter work for a client, the producers of The Hunger Games film franchise are planning more movies even after the second Mockingjay film is done. It looks like they're leaning toward new characters in the pre-existing universe rather than trying to come up with more adventures for Katniss, whose story is pretty much done with Mockingjay.
(Not going to go into any more detail for spoiler reasons.)
Although this looks like a blatant cash grab, it could actually be pretty interesting. Here are some ideas I just spun off the top of my head:
*A prequel about Haymitch Abernathy--how he became a victor, how his family was murdered in reprisal for his figuring how out to use the Arena itself as a weapon, and how he started the path toward becoming the ornery drunk he is. To make things even more interesting, he'd competed in a previous Quarter Quell where the Capitol demanded twice as many tributes as usual. It'd basically be the first movie with twice as many tributes and (apparently) twice as much brutality, with a male protagonist and a downer ending I won't be getting into for reasons of spoilers.
*The rise of the evil Capitol President Coriolanus Snow. He apparently murdered and manipulated his way into power, so he could be a Villain Protagonist. Think a sci-fi version of House of Cards set in probably one of the most thoroughly vile fictional societies ever created. Given how Snow apparently prostitutes victors to the other decadent aristocrats of the Capitol, this is something that could get into serious rated-R territory here.
*The rise of the Capitol and how it took control of the Districts and established the exploitative system that presumably provoked the first rebellion. If things were really so dark and desperate that one can make any case that the Capitol's system was needed to save humankind (at least in North America) from extinction, this could have a lot of Grey and Gray Morality going on.
*The first rebellion-This is when the Districts rebelled and after defeating them (with the exception of District 13, which made a separate peace), the Capitol imposed the Hunger Games on them. This could be really interesting, especially with the referenced rebel attack on the Capitol in the Rocky Mountains and how it was foiled by aerial bombardment. It could be a Hope Spot (like the scene in Valkyrie where all the top Nazis are getting rounded up and the viewer actually thinks the coup will succeed) followed by a massive downer when the attack is defeated and/or when District 13 betrays the rest of the rebels. This could be so epic it could be made into multiple movies.
Life lesson for writers--create worlds so detailed and "big" that you can write lots of stories set in this world, not just stories about the important characters. This is by no means advice to scrimp on characterization though--I doubt The Hunger Games could be the phenomenon it is now if not for the character of Katniss.
Producers of The Hunger Games, if you read this, please don't discard any of the above ideas for legal reasons. I've heard that Hollywood people sometimes ditch good ideas that they find others have come up with due to fear of lawsuits. Remember, ideas can't be copyrighted.