The Public Company Accounting Oversight Board has proposed a new policy that would entrust international counterparts to carry out the inspections of non-American accounting firms that audit U.S. public companies.

The proposed change to one of its policies follows the expansion of audit-firm oversight bodies not unlike the PCAOB springing up around the world. “The PCAOB recognizes that cross-border cooperation is fundamental to strengthening audit quality globally,” said chairman Mark Olson. The policy statement approved at the board’s Wednesday open meeting could lead to increased “reliance on the inspections of foreign counterparts, including our counterparts in the European Union.”

Three years ago, the PCAOB passed its rules for overseeing public accounting firms not domiciled in the United States. The idea behind the rules was to affirm the PCAOB’s right to inspect foreign firms while at the same time respecting that those firms shouldn’t have to be burdened by dual regulators. The firms are first and foremost inspected by their own country’s regulators, and the PCAOB has joined those regulators’ inspectors as a secondary regulator.

The proposed policy statement to be added to those rules would give the PCAOB room to give a foreign regulator “full reliance,” meaning that regulator would be entrusted to do field work and to do inspections on its own, and provide the PCAOB with an inspection report for each firm it inspects that audits U.S. companies.

The PCAOB would decide whether to give another oversight body “full reliance” after considering whether it fulfilled certain criteria, such as having an investor-protection mandate, a quality-assurance inspections program, and enough staff expertise and experience in the audit field.

The measure doesn’t come without reservations. Kayla Gillian, who plans to leave her board post in January, worries that the differing independence standards for international regulators do not match the intent of the framers of the Sarbanes-Oxley Act. The 2002 law led to the creation of the PCAOB and its staffs’ independence from the industry it regulates.

The PCAOB operates on a full-time basis, and its board members and staff can’t be affiliated with any accounting firm; however, the overseas regulatory bodies don’t have the same requirement, partly because of practicality. Many of the bodies are part-time and thus can’t afford to not have staffers that work at accounting firms.

Another board member, Charles Niemeier, dissented on the vote for bringing forward the proposal for a 90-day comment period, saying it goes too far. “The fact is that few if any countries spend as much on — or devote as much intensity of effort to — enforcement of financial reporting and auditing as the U.S. does,” he says.