(CNN) House Democrats are pushing forward on their investigations into President Donald Trump's finances — an area they feel special counsel Robert Mueller's investigation did not fully probe — adding additional senior-level investigative staffers and preparing to go to court to enforce their subpoenas.

The House Intelligence Committee has hired Patrick Fallon, a 25-year FBI veteran who was chief of the FBI's financial crimes section, according to three sources familiar with the matter, adding to their arsenal of staffers with experience prosecuting financial crimes and cases against Russian organized crime. Fallon started this week, according to a committee source.

The House Intelligence and Financial Services Committees are zeroing in on Deutsche Bank as a key part of their investigations into Trump's finances. Trump, his children and his business on Monday sued both Deutsche Bank and Capital One to block subpoenas that the committees have issued, but House Democrats are likely to fight those in court.

"Deutsche Bank is willing to cooperate, but apparently Mr. Trump and others around him are concerned about what those bank records would show," House Intelligence Committee Chairman Adam Schiff told CNN Tuesday. "We're going to have to fight this as vigorously as necessary to make sure that we validate our ability to oversee the administration."

The subpoenas for Deutsche Bank and Capital One are just one element of a broad House Democratic effort to probe Trump's finances — and one that the Trump administration is fighting at every step. The Trump Organization has also sued the House Oversight Committee and his own accounting firm, Mazars USA, after the House Oversight Committee issued a subpoena for years' worth of Trump's financial records from the accounting firm.

And the Treasury Department has missed a deadline from House Ways and Means Chairman Richard Neal to provide Trump's personal and business tax returns, in another dispute that's likely to end up in court.

"I do think that we intend to respond," Neal said.

Schiff has come under fire from congressional Republicans after Mueller's investigation ended, who have accused him of claiming to have evidence of collusion between Trump's team and Russia when Mueller did not establish any criminal conspiracy.

But Schiff has argued that the contacts that were unearthed between Russians and Trump's team are alarming, even if they aren't criminal, and he's also pointed to Trump's finances as an area that's ripe for further investigation beyond Mueller.

"We have to make sure that the President is operating in America's best interest not because he has some financial interest involved," Schiff said Tuesday.

Deutsche Bank and the Trump Organization

"We're not interested in whether he was a good business man or a crooked businessman," Schiff added. "We are interested in whether there is any financial entanglement -- whether that is with the Russians or the Gulf or others that is driving US policy because of the President's financial interest overseas, or his son-in-law's, or anyone else's, and we would be negligent in our oversight if we didn't make sure."

Deutsche Bank has about $300 million in loans extended to the Trump Organization. The German lender is one of the few large banks willing to do business with the real estate developer. The bank has not extended new loans to the company since Trump has taken office.

Trump's attorneys said in a statement Monday that the subpoenas to Deutsche Bank and Capital One were "unlawful and illegitimate."

"They seek information going back decades from anyone with even a tangential connection to the President, including children, minors and spouses," Trump's legal team said. "Every citizen should be concerned about this sweeping, lawless, invasion of privacy. We look forward to vindicating our clients' rights in this matter."

But Congress isn't the only entity seeking Deutsche Bank records.

Last week, CNN reported that the bank was complying with a subpoena from New York Attorney General Letitia James for documents related to loans made to Trump and his business.

Hiring experts in financial crimes

The decision to hire Fallon, the FBI veteran who ran the FBI's Financial Crimes Section, is another sign of the Schiff's focus on financial issues his broader investigation into Trump and the Trump administration.

Schiff in March announced he had hired Daniel Goldman as the committee's director of investigations. Goldman was previously deputy chief of the organized crime unit for the Southern District of New York, where he prosecuted cases against Russian organized crime.

Schiff has also hired aides with experience working for the FBI, the intelligence community and on the National Security Council. The hiring of a former NSC official prompted and angry response from Trump, who tweeted in February that Democrats were "stealing people who work at White House!"