Other changes to regulation, some put into place and others still under consideration, range from making it easier for big banks to pass the Fed’s annual “stress test” of their financial health to allowing some to borrow more. One idea being floated could quietly reduce capital levels at the biggest American banks over the course of the business cycle.

The tinkering is being driven by Randal K. Quarles, the Fed’s vice chair for supervision, whom President Trump nominated in 2017, and the effort has earned the consideration of Jerome H. Powell, the Fed chair. At a news conference last month, Mr. Powell said the Fed was weighing a proposal that might have the effect of reducing average capital levels at big banks over time.

Bolstering capital at large banks was a centerpiece of postcrisis efforts, as regulators looked for ways to ensure that banks would have stable sources of financing in the event of another downturn. In a crisis, depositors and creditors may demand that a bank return their money, destabilizing the financial system. Indeed, that helped to fell Lehman Brothers, the investment bank that collapsed in 2008.

But capital — money raised from shareholders or retained as profits — does not have to be repaid. The 18 biggest banks, which include American firms like JPMorgan Chase, Goldman Sachs, Citigroup and Bank of America, added more than $650 billion in common equity capital from the beginning of 2009 through the end of last year.

Bankers acknowledged that capital needed to be higher after the 2008 crisis, but increasingly say enough is enough. Big banks have complained of measures that might increase capital from current levels or that could make year-to-year requirements fluctuate more, and have criticized United States rules for being more demanding than international standards.

Bank lobbying groups like the Bank Policy Institute have pushed back on calls to lift capital requirements, saying that stricter regulations “would harm economic growth with little benefit to the safety and soundness of the financial system.” And the country’s large banks have been working for more than a year to persuade the Fed to avoid putting more stringent capital rules in place.

Representatives from each of the biggest banks have met multiple times with Fed officials to talk about the stress capital buffer, a measure that would condense and streamline capital requirements, according to two people familiar with the matter. Each bank also used a public comment period in 2018 to send letters detailing specific suggestions for changes the Fed could make when it enacts the new standard.