Robert Mueller’s stock is about to go up on Capitol Hill — or at least, it’ll go up in the newly Democratic-controlled House. After a two-month stretch where Mueller’s investigation into Russian meddling in the 2016 election barely made headlines and was notably absent from the campaign trail, some Democrats are now vowing to do everything in their power to protect the special counsel as he enters what may be the final phase of his work.

At the same time, Democrats are also promising to begin aggressive investigations of their own. Adam Schiff, the incoming House Intelligence Committee chairman, says he plans to reopen the panel’s probe into Russian interference in the 2016 election, starting with a list of 70 people, organizations and companies that he and other Democrats believe the GOP failed to examine fully. This is both good and bad news for special counsel Robert Mueller: On the one hand, Democrats’ desire to get to the bottom of what happened in 2016 could help fortify his work, especially after supervision of the Russia investigation was transferred last week to acting attorney general Matthew Whitaker, who has been openly critical of the investigation. On the other hand, it could create new headaches for Mueller or even undermine his work.

How the Democrats could help Mueller’s investigation

The most obvious benefit to Mueller is that Democratic control of the House presumably makes it more difficult for President Trump to oust the special counsel or shut down the probe early. There’s talk, once again, about passing a bill that would allow fired special counsels to appeal their dismissal to a panel of judges and potentially be reinstated. This legislation, which has been floated many times as protection for Mueller, remains out of reach unless Senate Republicans support it, which is possible but seems unlikely.

But Democrats don’t need Republican buy-in to exercise their newfound subpoena power. With this option in their toolkit, they can demand oversight if it appears that Mueller’s investigation is being stymied or important information is being suppressed. Some Democrats are already promising to call Whitaker, Trump’s controversial replacement for Jeff Sessions, to testify about his “expressed hostility” to the Mueller probe, and they’ve sent requests asking top Trump administration officials to preserve documents and evidence related to Mueller’s probe and Sessions’s resignation. Democrats could even end up calling Mueller to testify before Congress about his findings. This is especially likely if he’s fired.

It’s also possible that Mueller could learn something important from Democrats, especially if they do begin aggressively investigating issues that might fall under Mueller’s purview — like the infamous June 2016 meeting at Trump Tower. Paul Rosenzweig, a senior fellow at the R Street Institute who worked on the Whitewater investigation, said that special prosecutors have worked symbiotically with Congress before and have benefited from valuable information unearthed by a congressional investigation. For example, as the Watergate scandal unfolded, it was Senate investigators who discovered that the White House had a secret taping system. Rosenzweig cautioned that this kind of cooperation was rare, however.

Granted, Mueller has already been at work for 18 months, so this kind of blockbuster revelation might not be forthcoming. Democrats are, however, now in a position to send Mueller transcripts of interviews conducted with people who previously testified as part of the House Intelligence Committee’s Russia investigation. This could give Mueller cause to consider potential perjury charges.

Additional pressure from Congress could also help persuade key witnesses to cooperate. “Being implicated in both a congressional and law-enforcement investigation is a big deal, in terms of your anxiety, your stress level, your decision-making,” said John Q. Barrett, a professor at St. John’s University School of Law who worked on the Iran-Contra investigation. “It gives people more reasons to be cooperative.”

So, it’s possible that the Democrats could aid Mueller’s investigation by protecting the integrity of his work, providing him with additional information and perhaps convincing people who know important information to share it with the special counsel. But Democrat-led investigations into Russian interference in 2016 could also backfire.

How the Democrats could hurt Mueller’s investigation

Remember the Democrats’ newfound subpoena power? Turns out, it’s actually a double-edged sword. If Democrats begin summoning people to testify who are witnesses in or targets of the special counsel investigation, they could derail key parts of Mueller’s strategy. The most disruptive step Democrats could take would be to offer immunity to people Mueller is still in the process of questioning or prosecuting. And it has happened before: As part of its Iran-Contra investigation, Congress offered immunity to two former Reagan administration officials — John Poindexter and Oliver North — in exchange for their testimony about secret arms sales to Iran. The decision, which was strenuously opposed by the Iran-Contra independent counsel, ultimately resulted in both convictions being thrown out.

But let’s say immunity isn’t on the table. Holding public hearings with people who are in Mueller’s orbit could still cause problems for the special counsel, according to Katy Harriger, a political science professor at Wake Forest University who studies the history of independent counsel investigations. “There’s this perennial tension between congressional investigations and special prosecutors because Congress’s goal is to shed light on everything, while it’s much better for Mueller to keep what he’s doing secret until he issues his indictments,” she said.

So far, Mueller has been extremely successful at keeping the details of his investigation quiet. Reporters track the comings and goings of witnesses at his grand jury, but the details of what Mueller has learned and his overall strategy remain a mystery to observers, including the people who may be implicated. But public hearings could change this dynamic completely, allowing witnesses to coordinate with each other about the story they’re telling investigators. Congressional hearings could also produce testimony that conflicts with Mueller’s findings.

Communication with Mueller’s team could help the Democrats avoid some of these problems, but Barrett said that it might be better for them to avoid bringing in high-profile witnesses until Mueller’s investigation is complete. Instead, Democrats could start by subpoenaing documents and financial data that shed light on the events of 2016 without requiring someone like Roger Stone — the former Trump campaign official who claimed to be a pipeline to WikiLeaks — to testify publicly.

But if history is any indication, Mueller might want to brace himself for unwanted interference. “The Democrats will want to tread carefully, because we’ve had a long history of congressional investigations that were at cross-purposes with independent counsel investigations,” said Rosenzweig. However, legal experts like Rosenzweig say that there are many avenues that House Democrats can pursue that won’t step on Mueller’s toes, like investigating whether Russia has leverage over Trump’s financial interests.

In the end, if Democrats don’t want to disturb or undermine Mueller’s work, the best course of action might be the simplest (and one they’ve advised Trump to take many times over the past 18 months): Leave Mueller alone.