The Department of Justice and four states on Monday filed a multibillion-dollar fraud suit against the Education Management Corporation, the nation’s second-largest for-profit college company, charging that it was not eligible for the $11 billion in state and federal financial aid it had received from July 2003 through June 2011.

While the civil lawsuit is one of many raising similar charges against the expanding for-profit college industry, the case is the first in which the government intervened to back whistle-blowers’ claims that a company consistently violated federal law by paying recruiters based on how many students it enrolled. The suit said that each year, Education Management falsely certified that it was complying with the law, making it eligible to receive student financial aid.

“The depth and breadth of the fraud laid out in the complaint are astonishing,” said Harry Litman, a lawyer in Pittsburgh and former federal prosecutor who is one of those representing the two whistle-blowers whose 2007 complaints spurred the suit. “It spans the entire company — from the ground level in over 100 separate institutions up to the most senior management — and accounts for nearly all the revenues the company has realized since 2003.”

Education Management, which is based in Pittsburgh and is 41 percent owned by Goldman Sachs, enrolls about 150,000 students in 105 schools operating under four names: Art Institute, Argosy University, Brown Mackie College and South University.