It remains to be seen whether Crapo’s efforts will win the backing of House Republicans, who must also approve the bill for it to reach President Donald Trump’s desk. Last year, the House passed much more sweeping legislation that would rip up much of Dodd-Frank. If some House GOP members demand a more aggressive rollback, Senate Democrats could walk away, causing the legislation to fail.

House Headwinds?

In a sign that there still could be issues that need to be ironed out, House Financial Services Committee Chairman Jeb Hensarling, a Texas Republican, said in a Wednesday interview that there are about four dozen bills that the House has already passed that he would like to see added to Crapo’s legislation.

The version Crapo released Wednesday puts to rest questions about whether the biggest foreign banks doing business in the U.S. -- such as Deutsche Bank, Barclays and HSBC Holdings Plc -- would piggyback on the major break mid-sized lenders are poised to get from post-crisis oversight.

It clarified that foreign banks with more than $100 billion in consolidated U.S. assets will still be subject to aggressive monitoring by the Federal Reserve, echoing what Fed officials including Vice Chairman Randal Quarles have said in recent public remarks.

The move follows criticism from some Democrats that Crapo’s legislation could free non-U.S. banks from stress testing and other burdens -- leaving them “mostly deregulated,” according to Senator Sherrod Brown of Ohio. One of the key requirements for the largest foreign banks was to set up “intermediate holding companies” in the U.S., and the latest version of the bill keeps such a requirement in place.

Intense Lobbying

Industry groups have been lobbying right up to an expected Senate vote to persuade lawmakers to amend a provision in the bill on what’s known as the supplemental leverage ratio, a change that could free up billions of dollars for Wall Street banks. The amendment Crapo released Thursday indicates the campaign failed, as custody banks such as Bank of New York Mellon and State Street that safeguard assets for their customers remain the only firms getting relief.

Still, the Fed is separately working to relax the capital requirement in a way that would benefit more lenders. The Congressional Budget Office estimated in a report earlier this week that there’s a 50 percent chance that the Fed will relax the rule for Citigroup and JPMorgan Chase & Co. should Congress pass Crapo’s bill.

For years, big banks like Goldman Sachs have been trying to relax the Volcker Rule’s ban on proprietary trading. While most of their focus has been on regulators, one change they’ve sought from lawmakers is reducing the number of agencies with authority over the rule. That, in turn, could make it easier to soften its impact. Crapo has declined to provide such relief in his legislation.