I've gone through the entire process for one story and am ready to write it. But I want to write the novel in a first-person point-of-view (from the Main Character/Protagonist's POV). With this POV, I don't see how I can present the Influence Character's throughline. It is how the audience would view the Influence Character; yet, the storytelling is colored always by the Main Character's POV. The Main Character's story line and the Relationship Story throughline are easy. The Objective Story throughline is working (although somewhat colored by the MC's POV, too.)
Concerning your question about the Influence Character POV in a predominantly Main Character (first person) story, there are several points to consider. The first and foremost is the relationship between the MC and the IC (the Relationship Story Throughline). The MC has a perspective (world view) that comes into conflict with the world around him/her. The IC is defined by his or her alternative perspective (or world view), and by how that alternative impacts the MC. One of the two perspectives, the MC's or the IC's, will make better sense and have a better feel than the other. Ultimately, one perspective will give way to the other (for better or worse).
It is easy to illustrate the alternate world view, even from the first person narrative form. For example, Jay Gatsby in The Great Gatsby is the Influence Character to the MC and narrator, Nick Carraway. Nick Carraway was raised to be tolerant of other's moral shortcomings. By his presence, Jay Gatsby forces Nick to reconsider this long held belief. Ultimately, to quote our story analysis, "The events that occurred in the summer of '22, however, gave him an aversion to the ways of the corrupt and dissolute, and his essential nature changed."
The narrator's "voice"--no matter which character "vocalizes" it--is that of the author. This means that a narrator, by definition, is not part of the story while they are narrating. So, if the narrator says, "A long time ago in a land far away..." it is not the Character speaking, but the author talking ABOUT the story, not speaking from within the story. (By Story, I mean a Grand Argument Story, not the type of "work" in which it is expressed, such as novel, screenplay, ballad, etc.)
Voice vs. Perspective
So now let's talk about the writer's use of voice (first person, second person, etc.) versus the four perspectives in a grand argument story.
An author can choose to tell a grand argument story using only one writer's voice, or several.
Let's use the fairy tale of Little Red Riding Hood (LRRH) as an example. Specifically, let's examine the event where LRRH first meets the wolf.
What are the four throughlines?
Main Character: Little Red Riding Hood
Influence Character: Wolf
Overall Story: LRRH is taking goodies to her ailing Grandmother when she is waylayed by a wolf.
Relationship Story Throughline: Predator/Prey
Now let's describe all four throughlines using the First Person writer's voice:
MC: "I was skipping along through the forest when a big, black wolf jumped out from behind a tree and blocked my path. I was so startled, I almost dropped my basket of goodies! Boy, was he a good-looking wolf."
IC: "I could see that you liked me by your staring glaze and crooked smile. You wanted more from me than what was in my basket. My mother had warned me about wolves like you."
OS: "What I didn't see was that there was a hunter with a big ax that was searching the forest for the wolf. It seems that the wolf had killed several of his sheep the night before. The wolf knew the hunter was nearby and that made him very nervous."
MC/IC: "The more I thought about it, the more it seemed that the wolf and I had a lot in common. We were both alone together on a desolate forest path, looking for companionship. Sure, he might see me as a tasty morsel, but who says he so safe from he? You know, I think we might make quite a pair...given the right circumstances."
So, for the little examples above, you can see that the four throughlines can be expressed from the first person perspective. In the MC example, the narrator expresses personal (I) observations and feelings. In the IC example, the narrator expresses what the Wolf thinks and feels, and more particularly how the Wolf impacts the MC. In the OS example, the narrator describes events that she could not possible see as LRRH. That's what is meant by the "big picture." In the Relationship Story example, the narrator describes the relationship between LRRH and the Wolf.
You could choose to express the throughlines exclusively in the first person voice, such as the examples above, or you may choose to express them using different voices. Using multiple voices is much trickier because it can be jarring to the reading experience for the audience, but it is a completely viable alternate to the more common "one work--one writer's voice" practice. You may also use the second person voice and third person voice (more traditional) to tell your story.