The Senate impeachment trial of President Trump may have ended with an acquittal, but ongoing legal battles and talk of future subpoenas hint that the drama between Congress and the White House is far from over.

Senate Minority Leader Chuck Schumer, D-N.Y., was dismissive of Trump's acquittal, calling it "virtually valueless" and the result of "one of the largest cover-ups in the history of our nation." And remarks from multiple House Democrats show that they are still looking for more information they can use against the president.

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Meanwhile, the president delivered celebratory remarks with supporters on Thursday as his White House declared vindication, maintaining as he did throughout the impeachment inquiry and trial, that he "did nothing wrong."

But one matter could result in new developments as early as Friday, with the D.C. Circuit Court of Appeals expected to issue a ruling in the near future regarding whether the House Judiciary Committee can compel the testimony of former White House Counsel Don McGahn.

In a court filing for that case, House Democrats revealed that McGahn's testimony related to information in the Special Counsel's Russia report could even be used for new articles of impeachment.

"If McGahn’s testimony produces new evidence supporting the conclusion that President Trump committed impeachable offenses that are not covered by the Articles approved by the House, the Committee will proceed accordingly---including, if necessary, by considering whether to recommend new articles of impeachment,” the committee's December brief stated, noting that they still have “ongoing impeachment investigations.”

According to former special counsel Robert Mueller's report, Trump had instructed McGahn to relay orders to have Mueller fired, which Trump's critics have said is enough to justify an obstruction of justice charge, although this was not included in the articles of impeachment that were the subject of Trump's recent trial.

The D.C. Circuit's ruling in that case could influence how House Democrats proceed with other avenues of investigation. Judiciary Committee Chairman Jerrold Nadler, D-N.Y., warned Wednesday that he may issue a subpoena for former national security adviser John Bolton in order to further delve into Trump's dealings with Ukraine.

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Rep. Madeline Dean, D-Pa., said Thursday that she spoke to Nadler and that she believes that Democrats "will be doing continuing oversight, including having Mr. Bolton."

When asked about this, House Oversight Committee Chairwoman Carolyn Maloney, D-N.Y., simply said, "Well, that's a topic we can discuss later," although days prior to Trump's acquittal she told Bloomberg, “The investigations and oversight will continue,” and made reference to "several cases."

Bolton had said he would comply with a Senate subpoena if he received one during Trump's impeachment trial, but House Intelligence Committee Chairman Adam Schiff, D-Calif., told MSNBC's Rachel Maddow Wednesday that after the Senate voted not to call witnesses, Bolton refused to submit a sworn affidavit.

Bolton has not commented on Schiff's claim.

The legal battles may not all be waged from the same side of the aisle, however, as Republicans are looking to punch back.

Days before Trump's acquittal, Senate Judiciary Committee Chairman Lindsey Graham, R-S.C., told Fox News' "Sunday Morning Futures" that in the coming weeks, Republicans would be investigating the anonymous whistleblower, whose complaint about Trump's phone call with Ukrainian President Volodymyr Zelensky led to the impeachment inquiry. Graham also said he wanted to look into Hunter Biden's dealings with Ukrainian energy company Burisma Holdings, and any potential conflict of interest with former Vice President Joe Biden.

Senate Finance Committee Chairman Chuck Grassley, R-Iowa, and Senate Homeland Security and Governmental Affairs Committee Chairman Ron Johnson, R-Wis., announced in a letter Wednesday they are seeking "records of Hunter Biden’s travel while he was under U.S. Secret Service protection as they continue to investigate potential conflicts of interest to boost his business ventures in Ukraine and China."

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House Speaker Nancy Pelosi has also been in the GOP's crosshairs. House Republicans introduced a resolution Wednesday against Pelosi after she tore up a copy of the State of the Union address Tuesday night.

The privileged resolution, introduced by Rep. Kay Granger, R-Texas, slammed Pelosi's behavior as “a breach of decorum and degraded the proceedings of the joint session, to the discredit of the House." The House on Thursday voted to table the measure.

Fox News' Brie Stimson, Andrew O'Reilly and Gregg Re contributed to this report.