Top financial regulators are considering adding large mutual funds, hedge funds and private equity firms to the list of institutions that are officially “too big to fail,” and some of those money managers pushed pack this week.

The Financial Stability Oversight Council, the supergroup of regulatory agencies created by the 2010 Dodd-Frank financial reform law to respond to systemwide threats to financial stability, moved a step forward Monday in deciding whether to label certain asset management firms “systemically important financial institutions.” That designation, an acknowledgement that a company is too big to fail without dragging down the rest of the system with it, carries with it higher capital requirements and stricter regulation.

Although banks with more than $50 billion in assets automatically qualify as "SIFIs," the oversight council has the authority to list any company systemically important and bring it within its regulatory purview. Last year, it gave that designation to three insurance companies, including AIG, which was at the center of the financial crisis. The FSOC began to research adding asset managers to the list of SIFIs in the fall, a move that has elicited worries from investment firms and members of Congress.

Separately, the Financial Stability Board, an international body coordinating top economies' financial regulation in which top U.S. regulators participate, is similarly considering adding certain investment funds to its list of systemically important firms.

Mary Miller, the Department of the Treasury's under secretary for domestic finance, said on Bloomberg TV ahead of the FSOC's meeting that the group had not determined whether it would label asset managers too big to fail. “There is no predetermined outcome, no judgments have been made,” Miller said, explaining that “this is a public exercise” intended to put all the “stakeholders” in one room.

Miller said, however, that no other government entities are considering whether mutual funds, hedge funds and other investment firms pose systemic risks, and that “there’s a range of remedies” to be considered if they do.

At the FSOC’s meeting in the Treasury, hedge fund manager Ken Griffin warned that the risks involved in asset management “just at the end of the day [don't] make the top 100 things we need to worry about as a society in terms of financial market stability.”

The asset management industry is large, with 11,000 investment advisers registered with the Securities and Exchange Commission in command of $16.2 trillion in assets, according to a presentation by an SEC official at Monday's meeting.

Some analysts, though, have said that asset managers pose no systemic threat to the financial system because they invest funds on behalf of investors, and are not subject to runs because they don’t rely on borrowed money.

Others have warned that the too-big-to-fail designation would raise costs for asset managers that would be passed on to their investors, a concern that Vanguard Chairman and CEO William McNabb echoed at a House hearing on the topic Tuesday.

Nevertheless, Federal Reserve Chairwoman Janet Yellen, an FSOC member, warned at a Senate hearing earlier in the month that “if these firms are systemic, their failure can cause financial instability problems.” She suggested that “that's a reason for them to be designated and subject to risk standards and … capital and liquidity standards that would reduce the odds that they could fail.”

Meanwhile, Republicans in Congress have objected to the FSOC’s designation process, which they say lacks transparency.

Warning that the FSOC is trying to move non-bank institutions “from the non-bailout economy to the bailout economy,” House Financial Services Committee Chairman Jeb Hensarling, R-Texas, said at the hearing Tuesday. He added that the “FSOC's perfunctory explanations” of its decisions “are typical of an unaccountable group of agencies that feels it need not justify their actions to anyone.”

New Jersey Republican Rep. Scott Garrett, who has introduced legislation that would subject FSOC meetings to the Sunshine Act and allow congressional members of committees with oversight of regulators to attend, said that “the FSOC itself is one of the greatest threats to financial stability that we face today.”