Theory: Is Fuka Kiryuin's grandfather the man known as Shirogane?
In Year 2, Volume 9.5, Fuka mentions that as a child—since her parents were constantly busy—she lived with her grandfather more than with them. She also notes that her grandfather wields enough influence to secure her entry into any university or job she desires. Furthermore, Fuka describes her relationship with her parents as problematic, noting that they won't grant her freedom because she bears the Kiryuin surname.
In Year 2, Volume 11, Fuka expresses a desire to become a politician. She recalls meeting many politicians during her childhood but remaining indifferent to them; the only one who truly interested her was Prime Minister Kijima. Given that she spent so much time with her grandfather back then, it is highly likely she met Prime Minister Kijima at his home.
Year 3 Special Short Story: Sae Chabashira and Chie Hoshinomiya — Anniversary Party
This story reveals the close relationship between Prime Minister Kijima and Shirogane; furthermore, given their positions, Shirogane likely holds significant influence over the high school.
P.S. You might wonder why she bears the Kiryuin surname if Shirogane is her grandfather. A simple analysis of the details shared above suggests that Fuka was born of a political marriage—a common practice among wealthy families—leading to the decision to use the Kiryuin surname instead of Shirogane.