What I'd love to say post-NFL season in the US is what the Australians do with Rugby league, and that's State of Origin. It's a series where the best Rugby League players from the states of Queensland and New South Wales play a series after their season is over and it's truly epic, it's bigger than the club game. In other words, the players play for the state where they're from/grew up.
Imagine seeing a game where you had Florida v Texas? or Pennsylvania v California. The NFL would never allow it, of course, but the NFL is strange in that they only play 17 games (for most teams. In other sports, like fellow high attritional Rugby, they play for the clubs AND their countries.
It would be epic to see something like State of Origin in American Football.