A version of this story first appeared in CNN's Impeachment Watch newsletter. To get it in your inbox, sign up for free here

(CNN) For months, investigators looking into Rudy Giuliani's business dealings in Ukraine have dug into everything from possible financial entanglements with alleged corrupt Ukrainian figures to counterintelligence concerns raised by some of those business ties, according to people briefed on the matter.

The counterintelligence part of the investigation indicates that FBI and criminal prosecutors in Manhattan are looking at a broader set of issues related to Giuliani, President Donald Trump's personal attorney, than has been previously reported.

The counterintelligence probe hinges in part on whether a foreign influence operation was trying to take advantage of Giuliani's business ties in Ukraine and with wealthy foreigners to make inroads with the White House, according to one person briefed on the matter.

Head here for more from CNN's Evan Perez, Sara Murray and Shimon Prokupecz.

The Latest

Fourth man allegedly involved in Ukrainian scheme in custody -- David Correia, one of the four men charged last week in an alleged campaign finance scheme involving associates of Rudy Giuliani, was arrested Wednesday morning at New York's JFK Airport, according to a spokesman for the US attorney's office in Manhattan. More from CNN's Kara Scannell

-- David Correia, one of the four men charged last week in an alleged campaign finance scheme involving associates of Rudy Giuliani, was arrested Wednesday morning at New York's JFK Airport, according to a spokesman for the US attorney's office in Manhattan. More from CNN's Kara Scannell Graham plans to ask Giuliani to appear before Senate Judiciary -- Senate Judiciary Chairman Lindsey Graham, a South Carolina Republican, told reporters Wednesday that he is going to write to Giuliani asking him to appear before the committee, adding "we'll consider whether to subpoena him and others later." LINK

-- Senate Judiciary Chairman Lindsey Graham, a South Carolina Republican, told reporters Wednesday that he is going to write to Giuliani asking him to appear before the committee, adding "we'll consider whether to subpoena him and others later." LINK Grand jury subpoenas former GOP congressman -- A grand jury has subpoenaed former Republican Rep. Pete Sessions of Texas on matters connected to Giuliani, dealings of Giuliani associates with Ukraine and efforts to remove Marie Yovanovitch as US ambassador to Ukraine, sources familiar with the matter told CNN. LINK

-- A grand jury has subpoenaed former Republican Rep. Pete Sessions of Texas on matters connected to Giuliani, dealings of Giuliani associates with Ukraine and efforts to remove Marie Yovanovitch as US ambassador to Ukraine, sources familiar with the matter told CNN. LINK OMB officials won't comply -- Acting Office of Management and Budget Director Russ Vought and Michael Duffey, the OMB's associate director for national security programs, have been asked to appear for depositions from the three committees leading the impeachment process, according to a source familiar with the requests. The two OMB officials have no plans to comply, according to a senior administration official. LINK

-- Acting Office of Management and Budget Director Russ Vought and Michael Duffey, the OMB's associate director for national security programs, have been asked to appear for depositions from the three committees leading the impeachment process, according to a source familiar with the requests. The two OMB officials have no plans to comply, according to a senior administration official. LINK Perry defers to his counsel -- Secretary of Energy Rick Perry said he would "follow the lead" of counsel on whether he will cooperate with his House subpoena for documents relating to Ukraine. LINK

New details on Pompeo's role

Former State Department senior adviser Michael McKinley testified Wednesday that he had repeatedly asked Secretary of State Mike Pompeo for a show of support for the ousted US ambassador to Ukraine, Marie Yovanovitch — but was greeted with silence, according to two sources with knowledge of his testimony.

Much of McKinley's testimony before the three committees leading the impeachment investigation focused on internal dynamics at the State Department, which previous witnesses have told lawmakers were upended by Rudy Giuliani's efforts to go around normal channels in Ukraine to target Yovanovitch and push for Ukraine to open an investigation into former Vice President Joe Biden and his son Hunter Biden. LINK

Yovanovitch defied the White House last week in testifying before Congress, where she told lawmakers that Trump wanted her removed from her post based on "unfounded and false claims."

In a blistering statement to the committee, Yovanovitch said she had been dismissed last spring because of pressure from Trump and "a concerted campaign against me."

Sondland set to testify

US Ambassador to the European Union Gordon Sondland , whose first scheduled appearance was canceled at the last minute due to objections from the State Department, is expected to testify under subpoena on Thursday, according to his lawyers.

Lawmakers have been eager to press Sondland about text messages he exchanged related to Trump's July phone call with Ukrainian President Volodymyr Zelensky and the freezing of foreign aid to Ukraine.

The Washington Post reported Saturday that Sondland is expected to tell Congress that Trump relayed to him directly in a phone call the content of a text message that Sondland sent denying quid pro quo.

New polling on impeachment

A majority of US adults support the impeachment and removal of President Donald Trump from office, a Gallup poll released Wednesday found, continuing a trend of recent surveys that have found increased support for the Democratic-led effort.

Fifty-two percent of Americans support impeaching and removing Trump from office, while 46% disagree. That's a 7-point increase from when Gallup asked in June about impeachment and removal after former special counsel Robert Mueller's investigation into Russian interference in the 2016 election.

The level of support for Trump's impeachment is much higher than it ever was for former President Bill Clinton and above that for former President Richard Nixon in all but a final poll taken before the 37th president's resignation, according to the Gallup survey.

Wednesday's poll follows four others in recent weeks that found public opinion is shifting on the impeachment inquiry.

Looking ahead

Friday

Deputy Assistant Secretary of Defense Laura Cooper is scheduled to appear before the congressional committees leading the House impeachment investigation, according to two congressional sources.

is scheduled to appear before the congressional committees leading the House impeachment investigation, according to two congressional sources. Friday also marks the deadline for acting White House chief of staff Mick Mulvaney and Energy Secretary Rick Perry to respond to subpoenas for documents.

Tuesday

The top US diplomat in Ukraine, Bill Taylor, is expected testify before House committees in the impeachment inquiry, per a GOP source.

Key documents

Need a refresher on what happened when? Check out the key documents CNN has annotated below:

You can also reference CNN's visual timeline and guide to the key players for more background.

What are we doing here?

The President has invited foreign powers to interfere in the US presidential election.

Democrats want to impeach him for it.

It is a crossroads for the American system of government as the President tries to change what's acceptable for US politicians. This newsletter will focus on this consequential moment in US history.