I don't really think that the Max Payne sequel fits into this. Their both pretty "dark "and "gritty".

So he's no family, he's an alcoholic and depending on your ending choice his new found love can run into a bit of a situation, it's still dark, and even if both of them are dark, it's still the second part and it's still dark, so by that it should stay.

In a franchise, it entails the second game that takes on a gritty and dark tone to distinguish it from the first.