The Bronx school filed the lawsuit Tuesday in Manhattan state Supreme Court.
The lawsuit says the private school is owed compensatory damages of at least $1.05 million for the two settlements.
The suit names Granite State and New Hampshire Insurance companies and Chartis Claims Inc., all divisions of AIG.
AIG did not immediately return a call for comment.
Thirty-one former students have alleged that the prep school for decades was plagued by teachers who sexually abused students.
The school says settlements have been reached with "the great majority" of victims.