WARNING: The following post contains plot spoilers from the movie Thor: The Dark World.
Think about it. Your protagonist grows and changes from Point A (beginning) to Point B (end) in the first book, and from Point C (beginning) to Point D (end) in the second, and so on (each of the blue lines). Meanwhile, he or she also changes from Point A to Point D in a bigger, overarching way (the green line).
One way to accomplish that change over a series is to raise the stakes in every subsequent book --- make the outcome even more important to your protagonist.
In the Beginning
In the first Thor movie, Thor starts out as an immature child, completely unfit to rule. He can't even hold a civil conversation with someone without starting a fight.
At stake in that movie is his pride, at first, and his identity --- is he the successor to the Asgardian throne, or unworthy of the honor?
By its end, he's sacrificed enough and matured enough to be deemed fit for rule some day.
Raising the Stakes
In Thor: The Dark World, the second movie in the series, we have to go somewhere with Thor's character again, or he becomes a static character (unchanging). Static characters are boring. Since Thor is now mature, stable, renowned, and fit to rule, something had to throw him.
So the writers upped the stakes.
First, the woman Thor loves is infected with (or possessed by) an evil, otherworldly substance that could kill her. Then, Thor's mother is murdered, and his father takes a mentally unstable turn. Thor has to get help from his brother Loki, who has proven untrustworthy before, because Loki has information that Thor needs. Finally, there's a ticking time bomb: as the alignment of the nine worlds approaches, the evil Dark Elves enact a plot to bring total darkness and destruction throughout the entire realm.
At stake, then, is Thor's continued integrity to be worthy of the throne, the family honor, the desire to avenge his mother and visit justice on her killers, the life of the woman he loves, and the existence of all nine worlds and the entire realm.
By story's end, Thor has accomplished everything with aplomb and even matured to another realization: despite being good at ruling, he has no desire to rule Asgard. His priorities are different, so he walks away from that opportunity.
But he wouldn't have grown to that new realization about himself and his abilities if he hadn't faced worse stakes in the second movie.
Have you thought about writing a series before? What's at stake for your protagonist in your first book? How could you up those stakes in the second book to put the protagonist on another trajectory to change and grow?