Speaking with Allo Cine, Tom Holland revealed there are two sequels planned:
Yes, there is what we call the arc of the character. There is still a lot of room for Peter Parker and Spider-Man, especially, to grow in the next two movies. He’s definitely not the finished article by the end of Spider-Man: Homecoming and I really look forward to exploring the different ways he can grow up and... go through puberty I guess. It’s going to be an exciting couple of movies...
There will be a Spider-Man 2 and 3... Yeah, well now you know, sorry Marvel. Whoops!
As the team at Collider points out, the deal between the MCU and Sony only extends through Spider-Man 3.0 Part 2. The studios may need to renegotiate their deal for Spider-Man 3.0 Part 3; Sony may decide to part from the MCU and do the third film themselves. This is assuming they don't just detonate the Spider-Man franchise and start over again yet again.
How do you feel about a new Spider-Man trilogy? Should they go to the old west? Should they just have a bigger Death Star? Should Tom Holland do an evil dance with evil emo hair? Let us know in the comments.