A watershed legal battle over the White House’s attempt to oust a sitting Federal Reserve governor has only just begun, but if President Trump gets his way, it could leave him with much more latitude to steer the central bank’s decisions on interest rates and its oversight of Wall Street.

Mr. Trump is already relishing the idea.

“We’ll have a majority very shortly,” Mr. Trump said at his latest marathon cabinet meeting about the Fed’s powerful seven-person Board of Governors. “So that’ll be great.”

Mr. Trump plans to appoint loyal individuals to that board, and he would need to fill just one more seat for the balance of power to tip further in his favor. If that happens, it would give the president immense sway over an institution that is supposed to operate independently from the White House.

The president could also gain substantial leverage over another part of the Federal Reserve system — the 12 regional banks whose officials take turn voting on policy matters. The central bank’s staff are vulnerable, too.

“With four on the board, the president and his administration can have a big influence,” said Gary Richardson, a professor of economics at the University of California at Irvine. “It gives them ways to push.”

That kind of power is desired by Mr. Trump, who has for months harangued the Fed to lower borrowing costs and has made little secret that he would like Jerome H. Powell, the Fed’s chair, to resign. But until August, the chances that Mr. Trump could so swiftly gain a majority of support on the board seemed far-fetched.