U.S. regulators’ efforts to step up oversight of systemic financial institutions beyond big banks could reignite a debate about the systemic importance of asset managers, says Fitch Ratings.

In a new report, the rating agency said recent proposals from the U.S. Financial Stability Oversight Council (FSOC) point to an effort to enhance market resilience with “meaningfully wider” regulatory oversight. The FSOC proposed to facilitate the designation of non-banks — such as broker dealers, insurance companies and infrastructure firms — as systemically important, and to establish a financial stability risk framework for these firms.

While the details of the proposals are still unclear, Fitch said firms that are designated as systemically important would likely face increased capital requirements and higher compliance costs.

This could, in turn, affect firms’ product offerings, business lines and the competitive landscape, it noted.

“[C]ertain large and leveraged hedge funds could attract greater regulatory scrutiny given their potential to pose broader systemic risk in times of market stress,” the report said.

Additionally, the effort to enhance oversight could revive a debate about the role of investment managers that primarily manage large pools of capital for other investors, which “raises questions about the extent to which managers themselves can have systemic implications,” it noted.

Other areas of the financial markets, such as the crypto sector, “seem ripe for further regulatory scrutiny following the bankruptcies and crypto-related stress experienced over the past year,” Fitch also said.