As a comic reader, I can see two good sequels come into this franchise. The first would be doing the storyline of Superior Spiderman, this was a controversial plotline that actually ran for awhile, where Peter Parker has his mind switched with a dying Doctor Octopus. What Doc Ock doesn't bargain for is when taking over Peter's mind he also relieves some of Peter's most life effecting memories and thus understands his "power and responsibility" as Spiderman. Its an at times hilarious, and always interesting take because he basically thinks he can be a better Peter Parker than the real Peter ever was, by using his superior intellect to be both a more efficient Spiderman, and a more successful Peter Parker(he launches his own company), but he is still Doc Ock, a narcissist and has no issue being way more violent with his foes.
The other great plot line that would be the follow up to that would be a real "Spiderverse" story where literally hundreds of Spiderpeople from different dimensions get together to fight a bunch of Spider Vampires that feed off Spiderpeople.