“We feel very comfortable, based on the advice we got from our lawyers, that it does not violate the law,” Anthony J. Guida Jr., EDMC’s senior vice president for regulatory affairs, said of the compensation plan. He added that it was reviewed by two law firms before it was carried out in 2003, and has been periodically evaluated since.

Mr. Nelson joined the company in 2007 and had nothing to do with designing the pay policy that went into effect in 2003, Mr. Guida noted. The chief executive before him was Jock McKernan, a former governor of Maine who still serves as chairman of the board. A company spokeswoman said neither Mr. Nelson nor Mr. McKernan was available for interviews.

Apart from the financial consequences for the colleges, the lawsuit could have political fallout: Mr. McKernan is married to Senator Olympia Snowe, a Republican from Maine whose 2010 financial disclosure form lists EDMC stock and options worth $2 million to $10 million. Scott D’Amboise, who is challenging her in the 2012 Republican primary, has called on Ms. Snowe to resign because she benefited from her husband’s receiving “millions of our hard-earned tax dollars.” Senator Snowe declined to comment.

This is the first time that prosecutors have joined a suit like the EDMC whistle-blower case, and the government’s unprecedented intervention in such a compensation case comes amid escalating controversy over for-profit colleges. Enrolling about 12 percent of the nation’s higher-education students, the colleges get a quarter of all federal student aid and account for nearly half of all student loan defaults. Last Friday, the Department of Education released new data showing that more than 15 percent of those who had attended for-profit colleges defaulted within two years — twice the rate of those who attended public institutions, and three times as many as those who went to private not-for-profit colleges.

Harris Miller, president of the Association of Private Sector Colleges and Universities, said the for-profit colleges’ higher default rates were in part attributable to their serving lower-income students than other institutions.