Could a Republican president of a Federal Reserve bank teach Bernie Sanders and Hillary Clinton a thing or two about reforming the financial industry?

Neel Kashkari is the new president of the Federal Reserve Bank of Minneapolis. A former assistant secretary in the Treasury Department under President George W. Bush's administration, he is a self-described "free market" and "pro-growth" Republican. And in his first big speech in his new role on Tuesday, he shocked the banking community by essentially saying that the financial reform bill Dodd-Frank was an honorable effort, but didn't go nearly far enough.

He called for banks to be broken up into "smaller, less connected, less important entities," and pushed for imposing big new capital requirements on financial firms: "Turning large banks into public utilities by forcing them to hold so much capital that they virtually can’t fail," as he put it.

This is not just outside of Republican orthodoxy, it's to the left of the Democratic candidates running for president. But it's actually a pretty great idea, and both Clinton and Sanders should steal it.

To date, Hillary Clinton has been more cautious than Kashkari. She wants to reinforce Dodd-Frank's regulatory overhaul and add a risk fee on to the biggest banks to encourage them to slim down. On capital requirements, the furthest Clinton has gone is to say she might ask regulators to ratchet up the requirements by an unspecified amount. Bernie Sanders is closer to Kashkari's view — he is convinced the only thing that goes far enough is breaking up the biggest banks directly and reinstating the firewall between investment and traditional banking with a new Glass-Steagall Act — but he has never brought up the idea of turning banks into "public utilities," as Kashkari put it, by imposing capital requirements.

This is really the key idea in Kashkari's speech. Capital requirements are rules for how much shareholder equity a bank must have on hand compared to how much they've loaned out. Having that capital on hand is an insurance policy in case the firm's bets suddenly go bad, a la 2008. The higher the capital requirement, the more insurance it provides. And between Dodd-Frank and new international rules, capital requirements start at 6 percent and then rise to over 7 percent for the biggest financial firms. But what if we went bigger — much bigger?

There's been bipartisan support in the Senate for taking capital requirements for the systemically important financial firms— i.e. the "too big to fail" ones — to 15 percent. Even Jeb Bush offered a (very confused) endorsement of the idea. And some conservative thinkers have argued for taking it to 30 percent, which would be the kind of utility-style regulation Kashkari talked about.

All of that could make higher capital requirements a sneaky way for someone like Sanders to bust up the "too big to fail" firms. As the requirements increase, they make it harder for financial firms to be profitable. So a punishingly high capital requirement threshold for the too-big-to-fail banks would create a natural ceiling they'd want to get under. It would break up the banks by default.

Now Sanders thinks he can accomplish the same thing via Section 121 of the Dodd-Frank Act. And he could — in theory. As Mike Konczal, a fellow with the Roosevelt Institute who works on financial reform, told me: "If you get two thirds of regulators to say a firm is too big and too risky and we have to break them up, Dodd-Frank allows them to do it." Unfortunately, two-thirds of regulators is a lot of regulators. Restaffing the Federal Reserve and all the necessary regulatory agencies and getting them to vote accordingly would entail a huge, potentially unwinnable political battle, as would passing a new bill to break up the banks directly.

Worse for Sanders, reinstituting Glass-Steagall — the other idea Sanders had — needs a bank breakup to be effective. "It's not clear to me that removing investment banks by themselves part would be a huge size change," Mike Konczal said. "So you'd need to break them up as well to do what Sanders wants."

So you can see why Sanders should be intrigued by Kashkari's idea. But Hillary Clinton should be too.

Clinton is onto something by taking an "ecosystem" approach to financial regulation. Simply dividing investment banking and traditional banking, as Glass-Steagall did, is far too crude on its own to account for how risk moves through the modern financial industry. Dodd-Frank's extension of banking specific regulation to the entire financial industry — a new, wider net that Clinton wants to strengthen — was the right approach. And Dodd-Frank provides regulators tools to unwind a big firm if it's in a state of crisis.

But Kashkari is skeptical it's enough. "I learned in the crisis that determining which firms are systemically important — which are ["too big to fail"] — depends on economic and financial conditions," he said. "In a strong, stable economy, the failure of a given bank might not be systemic." But in a weak economy in a downturn, what size and interconnections could make a firm "too big to fail" could change dramatically.

"No rational policymaker would risk restructuring large firms and forcing losses on creditors and counterparties using the new tools in a risky environment, let alone in a crisis environment like we experienced in 2008," Kashkari continued.

So capital requirements can backstop much more of the risk in the system wherever it may reside, and super-high requirements for the systemically important firms could break them up, so they're already smaller and dispersed before a crisis hits. That way, when a crisis does hit, policymakers don't punk out and simply issue another bailout.

The politics are good for Clinton too: By explicitly calling for much higher capital requirements for the "too big to fail" firms, and explaining how those requirements are a long-game play to break them up, she could co-opt some of Sanders rhetoric and show his supporters she's listening.

As with health care, Sanders' strength is his lofty goals, and his weakness is his command of the practical details. For Clinton, it's exactly the opposite. Kashkari's capital requirements could be the fix they both need.