BOSTON — One father conspired to pay bribes to get two children admitted to the University of Southern California — one as a recruit in soccer, the other in football. A couple plotted to cheat on college entrance exams for their two daughters. A mother worried that her daughter might figure out she was trying to get her a fake ACT score, saying, on a call that turned out to be recorded by the authorities, “She already thinks I’m up to, like, no good.”

Four parents, including the former head of one of the world’s biggest asset managers and an heir to a fortune created by microwaveable snacks, pleaded guilty on Monday in the nation’s largest college admissions prosecution. With trials drawing closer and prosecutors warning of new charges, the four were part of a new wave of parents pleading guilty to using lies and bribery to secure their children’s admission to elite colleges.

Among them was Douglas Hodge, a former chief executive of Pimco and one of the most prominent business executives caught up in the scandal. He admitted that he conspired to pay more than $500,000 in bribes to get two of his children admitted to U.S.C. as athletic recruits.

“I accept full and complete responsibility for my conduct,” Mr. Hodge said in a statement. “I have always prided myself on leading by example, and I am ashamed of the decisions I made. I acted out of love for my children, but I know that this explanation for my actions is not an excuse.”