Two witnesses scheduled to testify this week in the House’s Ukraine probe could give both Democrats and Republicans more fodder for investigations, analysts say.

Kurt Volker, the former U.S. special envoy to the Ukraine who resigned his post last week, is set to appear Thursday before the House’s impeachment inquiry. Michael Atkinson, the intelligence community inspector general, will face questions from the House Intelligence Committee on Friday.

Both hearings are expected to shed light on President Trump’s dealings with Ukraine. Lawmakers have heavily scrutinized a July 25 phone call between Mr. Trump and his Ukrainian counterpart, Volodymyr Zelensky.

In the call, Mr. Trump suggests the Ukraine leader investigate 2020 Democratic presidential front-runner Joseph R. Biden. That call is the subject of a whistleblower complaint that has sparked an impeachment firestorm in Washington.

The two witnesses could give lawmakers on both sides a slew of ideas to further look at Mr. Trump’s dealings with Ukraine.

“They are presumably witnesses to different events and open up new avenues for investigation,” said Steve Schwinn, a professor at John Marshall Law School. “Volker was on the ground in the Ukraine so he may have some information that helps the House look into the matter or send the investigation into a different direction.”

Mr. Volker resigned after he was named in the whistleblower complaint.

Rudolph W. Giuliani, the president’s personal attorney, told reporters last week that Mr. Volker encouraged him to speak to Ukrainian officials regarding Mr. Biden, and his son Hunter.

Meanwhile, Mr. Atkinson is the inspector general who determined the whistleblower complaint was an “urgent concern” and “appears credible.” He likely has the most knowledge of the whistleblower complaint outside of the whistleblower.

Howard Krongard, a former State Department inspector general, said watchdogs such as Mr. Atkinson are typically more chatty in hearings than executive branch officials because they don’t have the same privilege concerns.

“An inspector general is expected to be more open than an executive branch official based on the operation of powers,” said Mr. Krongard, who frequently appeared before congressional panels.

The fact that Mr. Atkinson’s hearing is behind closed doors frees him to discuss confidential matters he could not raise in a public event, Mr. Krongard said.

For Republicans looking to help the president as impeachment efforts ramp up, the best-case scenario would be uncovering something scandalous about the Bidens’ activities in Ukraine, Mr. Schwinn said.

“That kind of information would be gold for the Republicans,” he said.

The younger Biden’s ties to lucrative Ukrainian natural gas contracts were investigated by a prosecutor in that country, but no evidence of wrongdoing was found. Still, Mr. Trump and his allies insist there was corruption afoot.

Democrats, meanwhile, are seeking evidence that Mr. Trump threatened to withhold military aid from Ukraine unless its leaders investigated the Bidens.

But they also need to hear from anyone who has first-hand knowledge of Mr. Trump’s dealings with Ukraine. The whistleblower in the complaint says he or she was not a “direct witness” to the incidents called into question.

“I think the Democrats need to hear concrete evidence from the White House about a quid pro quo or anything that would support that allegation,” Mr. Schwinn said. “The best case is they can secure first-party testimony from a witness who can support that narrative.”

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