MetLife scored a major coup earlier this year when it was able to persuade regulators to remove it from a list of institutions that are too big to fail and thus subject to tighter scrutiny. Now, some of its peers may face increased pressure to follow suit.

Shedding the onerous label of being a Systemically Important Financial Institution marked a milestone both for MetLife and the insurance industry. The list, an outgrowth of the financial crisis and an effort by regulators to rein in big Wall Street institutions, puts financial firms under the microscope of the Fed and the Financial Stability Oversight Council.