Yet while for-profit colleges are on the wane, there is another type of for-profit higher-education company whose profile and influence continues to expand. These new for-profits aren't seeking to run college programs themselves or win the traditional seal of accreditation. These companies do things like help traditional colleges start online programs, or offer colleges analysis on student behavior to help improve retention.

Call it the "Embedded For-Profit" sector in education, and it has become the darling of the venture-capital crowd and attracted billions in financial backing.

The emergence of this new sector also brings wide-ranging and yet-unexamined ramifications for colleges and policy makers, not to mention the taxpayers who indirectly subsidize these ventures.

It's 'Everywhere'

When for-profit higher education meant the University of Phoenix or an ITT Institute, many in traditional higher education largely dismissed it. It was "the other."

But these newer educational for-profits — selling things like interactive courseware and academic-advising engines — come much closer to teaching and other educational activities that colleges have long done for themselves. (A whole other universe of for-profits is springing up along the edges of academe, including coding boot camps.)

"Now, ‘for-profit’ is everywhere," says Jorge Klor de Alva, a former president of the University of Phoenix and currently president of the education-focused Nexus Research and Policy Center