If the Story Circle is how we imagine dealing with PLOT, then the FOUR CORNER CONFLICT is how we deal with THEME.
Theme is probably the most poorly taught part of the writing process. You hear about it a lot in school -- your teacher will ask you to identify what the theme of a book is -- but nobody will ever stop to explain what they mean by that. The closest an instructor ever came to telling me was saying "the plot is what happens in the book, the theme is what the book is ABOUT," but even that kind of falls flat. it doesn't tell you what that means or how to identify it, and I suspect a lot of people just struggle to explain it.
Put simply, the plot of the novel is what the characters are DOING. The theme is what they're arguing about or conflicting over. So, let's say you had a crime novel about a murder, and there are four main character: your protagonist, two secondary characters, and an antagonist. If those four characters are say, arguing about how far they should go to catch the murderer, then you have a plot of "murder mystery" and a theme of "the ethics of vigilantism" or maybe "order vs chaos." If you had that same plot but the same four characters were instead arguing about the how sympathetic they should be to the poor childhood of the suspect, then maybe your theme is "nature vs nurture" or even "how society judges those they cast aside."
But these seem normal if you're a fan of the crime genre. To really kind of prove the point, you have to make the example something outside the norm. So let's say you have a war movie in the trenches of World War II. Okay, that's your setting. And we give the men in that situation a mission, that's your plot. But then let's say one of them has a girl back home with whom he's gotten pregnant, and she's considering terminating the pregnancy. And now let's say he tells the men he's in the trench with and they all have different opinions on that and they conflict over those arguments. In this case, you have a War Movie, the THEME of which is the ethics of terminating a pregnancy, or (given the setting) a critic would probably simplify it down to "the ethics of ending life" or something of the like.
So, very broadly, the theme of a work ends up being the things the main characters conflict over. And the way we plan this conflict is with FOUR CORNER OPPOSITION.
In this planning method, you take the core beliefs you want to argue and you place them on a grid with their opposing argument: two columns, two rows. In doing so you've made a little 4x4 grid, and in each of those you place a character. That character's beliefs exist at the cross-section of their corresponding row or column.
So back to the fictional murder story above, maybe for the columns we put "By the Book" and "Willing to Break the Rules." And maybe for the rows we put "To Catch a Criminal" and "To Defend the Innocent." So now, each character has a defined way they will argue and act in each situation.
Character A's priority is to catch the criminal, and he'll do so by the book. Character B shares A's motives, but differs on methods. Character C has different motives from the previous two, in that they want to defend the innocent, but agrees with A that they should do it by the book. And Character D wants to defend the innocent at all costs, even if that means breaking the rules.
So when you put these characters is a room together, in any combination, you now know what they will agree on and what they will conflict over. And importantly, none of them are totally aligned. They will always conflict over something. In doing this we've created a lens where we can always explore any scene through conflict, which helps us move those scenes along.
Ideally, when figuring out your novel, you want at LEAST one of the characters from your four-corner grid in EVERY SCENE. Ideally you want two, because then they can conflict, but there would certainly be situations where a character would go off alone and do something privately so that it can become conflict later, but those scenes are sparse. You want at least two in every scene. Not only does this allow us to always have conflict, but because these core conflicts define what the theme of the book is, you will have a more thematically consistent book as a result as well. In the end it will be a book that is a better read for commercial purposes but also more easily analyzed and understood for critical purposes.