“We call it legalized corruption,” said Danielle Brian, executive director of the Project on Government Oversight. “And it permeates every aspect of federal government.”

King & Spalding is hardly unique. A new book by David Enrich, business investigations editor at The New York Times, details the deeply enmeshed relationship between the Jones Day firm and the Trump administration. Even that, however, is just a small part of the double take-inducing legal entanglements on display throughout Washington.

At Gibson, Dunn & Crutcher, for example, the partner Jose Fernandez provided legal services for both the Saudi sovereign wealth fund and Chevron until, last summer, he was confirmed as the State Department’s under secretary for economic growth, energy and the environment. Before that, Gibson Dunn welcomed back David Fotouhi, who once helped weaken environmental regulations as part of Mr. Trump’s Environmental Protection Agency and is now a member of the firm’s environmental litigation and mass tort practice group.

There’s Skadden, Arps, Slate, Meagher & Flom, where the former partner Gregory Craig — White House counsel under Mr. Obama and special counsel to Bill Clinton during his impeachment hearing — helped get a job for Paul Manafort’s daughter in what his lawyers described as an entirely normal bid to attract more of Mr. Manafort’s shadowy business. At the time, Mr. Craig and Mr. Manafort had been working together on a $4.6 million deal on behalf of the former Ukrainian president Viktor F. Yanukovych, who was known as Vladimir Putin’s man in Kyiv. (Mr. Craig was later tried and acquitted on charges that he lied to the Justice Department about his work for the Ukrainian government.)

The white-shoe firm Covington & Burling famously kept an office empty for Eric Holder, waiting for him while he served as attorney general under Mr. Obama. We may surmise that Mr. Holder returned to a hero’s welcome: The firm has represented several banks that his Justice Department investigated for their role in the subprime mortgage crash. Mr. Holder chose not to prosecute any executives, suggesting the financial catastrophe was the fault of corporate culture rather than specific individuals. Today Mr. Holder is promoting his new book on voting and voting rights, “Our Unfinished March.”

Then there was Mary Jo White, the Securities and Exchange Commission chair under Mr. Obama, who also worked at Debevoise & Plimpton, a law firm with deep ties to Wall Street. Ms. White was harshly criticized by Senator Elizabeth Warren for going soft on financial firms, and for repeatedly having to recuse herself due to the many conflicts of interest created by her corporate work. In the end, Ms. Warren tried but failed to persuade Mr. Obama to oust Ms. White.

Washington is full of operators who exert their influence and patch up political schisms so effectively that they create a sort of corporate shadow government that, arguably, functions more efficiently than the real thing.