Members of the Federal Reserve on Monday approved a plan that would give General Electric's finance arm a chance to shrink itself before it is regulated as if it were a big bank capable of bringing down the financial system in a failure.

The rule will facilitate General Electric Capital Corp.'s effort to avoid the added regulatory scrutiny that comes with being one of the four non-bank firms identified by regulators as "systemically important" companies that could drag down the financial system if they failed.

GE Capital's attempt to evade the label of "systemically important" is of significant interest to the financial industry and members of Congress who have worried that the designation is a regulatory "Hotel California," burdening companies with added regulations but providing them with no way out.

The Federal Reserve Board of Governors voted Monday for a two-stage plan for supervising GE Capital to allow for the possibility that it might go through with its plan, announced in April, to significantly shrink itself and thereby shed its "systemically important" label.

Speaking at the Fed meeting, Governor Daniel Tarullo said that "it would not be sensible for us to disregard GE's announced plan to reduce [General Electric Capital Corporation's] size by 70 percent, particularly in light of the fact that it is demonstrably executing that plan."

Under the plan, the firm would face the bare minimum capital and liquidity requirements starting in 2016 and wouldn't face the "full panoply" of Fed rules until 2018, Tarullo said. That would give GE Capital time to carry out its plan of selling off the majority of its assets.

If GE Capital is successful in getting the Financial Stability Oversight Council to reverse its decision to name the firm systemically important, it would never face the added regulations.

The council initially identified GE Capital as a systemic threat in summer 2013. The other three companies to receive that designation are all insurers: American International Group, Prudential and MetLife.

The council was created by the 2010 Dodd-Frank law to identify threats to the financial system originating outside banks. Republicans, however, have charged that its designation amounts to an official statement that those firms are regarded as "too big to fail." Members of the financial industry also have complained that the council risks undermining its own purpose if it does not provide companies with a path toward shrinking to avoid the label.