An appeals court panel hearing one of President Trump’s bids to keep his finances under wraps signaled Friday that the subpoenas issued by two House committees did not necessarily have to be all or nothing.

“We hear lots of appeals where one side says, ‘We want it all,’ and the other side says, ‘You don’t get any of it,’ but we’re not necessarily limited to those two options,” said Judge Jon O. Newman, one of the three judges on the panel of the United States Court of Appeals for the Second Circuit.

The arguments concerned subpoenas issued by two Democrat-controlled committees to Deutsche Bank and Capital One for years of records tied to Mr. Trump, his family and the Trump Organization. The House Financial Services Committee said it wanted the information to conduct a case study on money laundering in real estate, and the House Intelligence Committee said it wanted to know whether Mr. Trump’s financial dealings made him subject to foreign influence.

The subpoenas request documents related to Mr. Trump’s businesses, his in-laws, his children and even his grandchildren, which has prompted Mr. Trump’s lawyers to call them overly broad and lacking legislative purpose. They have also argued that the investigations amount to a law enforcement activity that is rightly the job of the Justice Department, which filed brief with the court this week offering the same view.