Stocks surged Tuesday after Treasury Secretary Janet Yellen indicated the government may be open to further assistance for troubled banks.

San Francisco’s First Republic closed nearly 30% higher as traders rushed to snap up bargain-priced shares of regional banks.

But what sort of assistance does the government have in mind?

At this point, Yellen is being noncommittal.

“There’s time to evaluate whether some adjustments are necessary in supervision and regulation to address the root causes of the crisis,” she said at a conference organized by the American Bankers Assn.

“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.”

Fair enough. But some Democratic lawmakers are saying it’s time to either raise the $250,000 cap on insured bank deposits or do away with the cap completely.

This, they say, would prevent runs on banks because all deposits would be covered.

And that’s undoubtedly true.

But here’s the thing: The vast majority of Americans have less than $250,000 deposited at banks.

Depositors who faced catastrophe at Silicon Valley Bank, Signature Bank and now First Republic Bank aren’t everyday folk. They’re businesses and wealthy people who, for whatever reason, deposited far more money than the government covers.

Lifting or abandoning the insurance cap, therefore, would primarily benefit well-heeled bank customers rather than working families trying to safeguard their financial assets.

And since the insurance coverage presumably would be funded by taxpayers, this potentially represents a massive safety net for the rich.

To be sure, such a move would be good for mid-tier banks, and it would help protect startups that can’t afford to lose access to funds, even on a short-term basis.

But they have an easy solution already. Banks can be more proactive in warning big-money clients that their funds are vulnerable unless they break them into separate accounts that don’t surpass the $250,000 limit.

And big-money clients can be smarter money managers, avoiding situations that expose them to massive losses should a bank fail. Again, separate accounts helps prevent trouble.

“Our intervention was necessary to protect the broader U.S. banking system,” Yellen said. “And similar actions could be warranted if smaller institutions suffer deposit runs that pose the risk of contagion.”

True. But she and other monetary authorities need to be very clear about who pays for such interventions.

And who prospers.