– 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. Another parent plotted to cheat on college entrance exams for his two daughters. A mother worried that her daughter might figure out that she was trying to get her a fake ACT score, saying, on a call that turned out to be recorded by authorities, "She already thinks I'm up to, like, no good."

Four parents — the former head of one of the world's biggest asset managers, the founder of a Silicon Valley finance firm, and an heir to a fortune created by microwaveable snacks — all pleaded guilty Monday in the nation's largest college admissions prosecution. With trials drawing closer and prosecutors warning of new charges, the three 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 USC as athletic recruits.

"I have always prided myself on leading by example, and I am ashamed of the decisions I made," he said. "I acted out of love for my children, but I know that this explanation for my actions is not an excuse."

The other parents who pleaded guilty Monday were Manuel Henriquez, the founder and former chief executive of Hercules Capital, a financial firm in Palo Alto, Calif., and Michelle Janavs, of Newport Coast, Calif., whose father and uncle invented the Hot Pocket. Henriquez's wife, Elizabeth, pleaded guilty later in the day.

More than a dozen parents caught up in the scandal, including actress Felicity Huffman, pleaded guilty months ago in connection with the cheating scheme revealed in March. But others among nearly three dozen parents charged, including Hodge, had entered not guilty pleas and, until now, appeared headed for trial.

According to several lawyers involved in the case, prosecutors gave some parents deadlines of Monday or a few days before to agree to plead guilty, or risk facing a new charge that had the potential to bring a longer sentence. These lawyers said they now expected prosecutors to bring that new charge — federal programs bribery — against most, if not all, of the parents who stick to their not-guilty pleas. Two lawyers said it was possible that additional parents would also be charged.

A representative for the U.S. Attorney's Office declined to comment.

Among the parents who have pleaded not guilty is actress Lori Loughlin. While magazines have reported that Loughlin was anxious about the case, there has been no indication that she intends to change her plea. A lawyer for Loughlin did not respond to a question about her plans.