Regional bank stocks rebounded Tuesday as Treasury Secretary Janet Yellen pledged further assistance to depositors if needed and a second attempted rescue of troubled San Francisco lender First Republic (FRC) took shape.

First Republic rose nearly 30% Tuesday, just one day after plummeting 47% to its lowest-ever closing price. The March 10 failure of Silicon Valley Bank put First Republic under tremendous investor pressure, and an infusion last week of $30 billion in deposits from 11 other banks didn’t stop the slide that continued through Monday.

One of those 11 banks, JPMorgan Chase (JPM), is now providing advice to First Republic as the bank seeks other options, said people familiar with the situation. Raising capital from outside investors is among the possibilities, these people said. Another is turning some deposits provided by bigger banks into equity, these people said.

Shares of other regional banks that received similar scrutiny in the wake of Silicon Valley Bank’s seizure also rose Tuesday. PacWest (PACW), Western Alliance (WAL) and Zions (ZION) were all up.

The regional bank bounce on Tuesday followed a pledge Yellen made before an American Bankers Association conference to take more actions to stabilize the banking system if needed. She and other government officials decided earlier this month to protect uninsured depositors at both Silicon Valley Bank and the failed Signature Bank, while also freeing up more liquidity in the banking system.

"The steps we took were not focused on aiding specific banks or classes of banks. Our intervention was necessary to protect the broader U.S. banking system," Yellen said in prepared remarks released by the Treasury. "And similar actions could be warranted if smaller institutions suffer deposit runs that pose the risk of contagion."

During a question-and-answer session at the ABA conference Tuesday, she said the current banking crisis "is different" than the 2008 financial debacle. "Rather, what we're seeing are contagious bank runs." The public, she added, "should have confidence in our banking system and it's our intention to remain vigilant in the days and weeks to come...that means potentially intervening if a smaller bank experiences the kinds of difficulties we've seen that pose the risk of contagion."

Treasury officials are studying whether they can expand a backstop provided by the Federal Deposit Insurance Corporation to all deposits without the approval of Congress, Bloomberg has reported. A bank advocacy group has asked federal officials to lift that $250,000 per deposit cap, according to Bloomberg.

Deposit outflows are a concern for followers of First Republic, which serves wealthy clients who are mostly clustered along the coasts.

S&P Global on Sunday downgraded the bank’s credit rating three notches deeper into junk status and warned it could go lower if the bank was unable to stabilize deposits, among other measures. The Wall Street Journal has reported that customers withdrew $70 billion in deposits from First Republic but that the outflow stabilized Friday following the announcement of $30 billion in new deposits from 11 banks.

First Republic is now looking to raise more capital, and JPMorgan is providing advice. One possibility, said people familiar with the situation, is that some of the deposits provided by the 11 banks could be turned into equity. The Wall Street Journal earlier reported JPMorgan’s assistance and the options under consideration. A spokesman for First Republic declined to comment.

Yellen on Tuesday said deposit outflows among banks, without mentioning any in particular, have "stabilized." When asked about the next steps, Yellen said: “there's time to evaluate whether some adjustments are necessary in supervision and regulation to address the root causes of the crisis. I don't want to speculate at this point on what those adjustments might be. What I'm focused on is stabilizing our system and restoring the confidence of depositors.”

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