Straight from the horses mouth on this one, it looks like we are going to have to wait a bit for the New Game + mode from Marvel's Spider-Man. There is a new update and a brand new chunk of DLC on the way, but it just isn't here yet. Be patient, Spider-Man lovers; go play God of War's new game plus in the meantime. You know you want to.
Here's what was said before, but this has since been deleted. The official word now is that the new modes are "coming soon".
“We are also thrilled to announce the release of Update 1.07* tomorrow, October 17, for Marvel’s Spider-Man owners around the world. While the team here has been working hard on the Marvel’s Spider-Man: The City That Never Sleeps DLC and its first chapter, Marvel’s Spider-Man: The Heist, we’ve also been working on free updates for the game that adds new features and fixes a few bug issues.
Update 1.07 is one we’ve been working on for a while now, and adds New Game+ (NG+) as well as Ultimate Difficulty to the game. NG+ allows you to play the story and all activities in the open world again with all of your unlocked suits, skills, gadgets, mods, and benchmarks from the beginning. While playing NG+, you’ll be able to unlock those final items while cleaning up your trophy list!
Speaking of that, we’re adding two new trophies as well – one for completing the game on Ultimate Difficulty, and the other for finishing a NG+ run!
Additionally, many of you have requested the ability to rotate Stickers in Photo Mode, and we’re pleased to let you know that’s included, along with a few additional bug fixes, in Update 1.07.We’ve also tuned Friendly Difficulty based on your feedback to be more friendly.”