The Consumer Financial Protection Bureau wants to expand its supervision of student loans to those servicers that operate outside of the banking system.

A new CFPB rule would give the agency new oversight over student loans from Sallie Mae, NelNet and a few state and non-profit agencies. Most student loans are processed by these non-banks. Starting in March, the government will gather reports and conduct exams on how they do business.

Altogether, the institutions subject to this new monitoring manage more than 49 million borrower accounts.

Americans owe more than a trillion dollars in student debt. And in the past year, watchdogs have been looking in to thousands of complaints. There have been lots of complaints that the institutions who collect people’s monthly payments try to maximize late fees and that paperwork often gets lost when loans are being transferred.

One of the biggest complaints involves what happens when a borrower has multiple loans she’s trying to pay back, all with different interest rates. People have complained that payments they make to knock out a specific high-interest loan, are instead getting spread out across all their loans.