This is really interesting. I'd be happy if it was released, even if its a poor effort it would still be a topic of discussion. But the question is, would a sequel be logical?
At the end of the original, the real ending, when Travis is hailed as a hero. Not the climactic bloody shootout. Travis is finally, on some level, at peace. Many have argued that this scene was a coma-induced dream, or for a different reason, not reality. But on second viewing you realize that doesn't matter, it's a fitting ending because Travis has finally escaped his inner demons, and on an emotional level, is content.
Now where would a sequel begin? Our most logical hint is the final moment of the film, where Travis drives Betsy home, Betsy flirts with him, he has forgiven her for rejecting him and is happy beyond words to be with the woman he wanted to (and now can) love. He drops her off, she walks inside, Betsy is no longer in his view. As he drives off, a sharp ringing sound drowns out the drone of the taxi, Travis adjusts his mirror to see what's going on, and stares behind him. It's hard to explain why when typing this out, but its entirely clear that this represents how despite his success in becoming a hero, his bout with mental instability will always be a step behind him.
So if there IS a part two, I only see one starting point. A brief catch-up scene which shows us what's happened since Travis put his demons behind him, and then soon after, their resurfacing. This story, being the plot of the sequel. If anyone else can think of a different plot, that would be cool. Because I can't.