What defines a protagonist?

So, I was fine-tuning the outline for The Men in the Black Coats (which, at this point, will be running for around a year and a half), and I realized something: the main protagonist, Rose, is only going to be in the story for a maximum of 59 chapters, while another character who isn't going to be introduced until around chapter 17 is going to be in at least 63 chapters, and a lot of the main action is going to center around her and her backstory. Rose isn't going anywhere, and is still going to be important, but the new character is going to be in the story more than Rose, and is going to be what moves the plot forward for almost 40 chapters. If things get out of hand, I could even see the entire focus of the story shifting to more of her viewpoint.

Has anybody else been in this sort of volatile situation where the protagonist accidentally stops being the center of their own story? Because I've never had any experience with this sort of thing, and I cannot seem to figure out a way to handle it.

Two thoughts:

1. The protagonist is the character whose choices shape the story. For example: Dr. Watson is the viewpoint character in Sherlock Holmes stories. Holmes is the protagonist.

2. You can have more than one protagonist. You're just setting yourself up to write a more complex story.

Sounds like you have two protagonists, nothing wrong with that. However keep in mind what Jim said, it will make things more complex. In my Overwatch stories the protagonist doesn't even show up in more than two of them physically, she is still the closest thing I have to a protagonist. Because of how important her choices are in the other stories. If your story needs two protagonists, then have two of them

Protagonist is Greek for first (main, chief) actor. It is a term that applies to stories with a main character. Stories can easily be ensembles or have multiple parts each with their own focal point. Lord of the Rings focuses on Frodo but also Aragorn, and sometimes Sam. Hamlet is about Hamlet, but a Midsummer night's Dream is about an ensemble. Star Wars could be about Luke, but the prequel trilogy makes all six movies about Vader, yet Han has a redemptive story arc as well.

In Psycho the protagonist dies halfway through and then her sister resolves the plot. Thinking in terms of a main character isn't necessary to a branching story so long as different scenes each have a solid focus.

I suggest reading more and broadly to see how it gets handled by other writers.