Tiny changes to a story can make a huge difference. This is starting from the very beginning. What if Harry made a couple of different choices right at the very start. Would everything change, or are some things just set in stone?
Muggle-borns do not just spring up out of no-where, they are descendants of Squibs of course. What if Hermione was contacted during the summer before starting Hogwarts and her lineage was discovered.
When Hermione decides that it's time to start preparing for the upcoming war she makes new friendships that could completely change the way she thinks.