After a week that could tally as one of the most turbulent of his presidency, Donald Trump and his embattled top aides have been hit with strong signs the worst is yet to come, in the form of tersely worded court documents and testimony.

On Wednesday, Trump’s ex-lawyer Michael Cohen, whose job for 10 years was, in his own words, to cover up Donald Trump’s “dirty deeds”, stood before a US district judge and described how his once-bulletproof faith in Trump had been shattered.

“I accepted the offer to work for a famous real estate mogul whose business acumen I truly admired,” Cohen, 52, said of the president. “In fact, I now know that there is little to be admired.”

But a less-noticed scene in court that day points to much bigger trouble ahead for Trump. Also present for the Cohen hearing was a member of special counsel Robert Mueller’s team, the prosecutor Jeannie Rhee, who described how much help Cohen had been to the investigation into alleged collusion between the campaign and Moscow.

“He has provided our office with credible information” about “core Russia issues”, Rhee told the court. “Mr Cohen has sought to tell us the truth, and that is of utmost value to us.

“There’s only so much that we can say about the particulars at this time.”

The “particulars” that the Mueller team declined to talk about almost certainly pertained to investigations with targets who ranked above Cohen, legal analysts said. Those could be one of relatively few figures at this point, experts agreed: probably one of the president’s children, his son-in-law, or Trump himself.

“There is no question in my mind that there is more to come from Robert Mueller,” the former federal prosecutor Renato Mariotti, host of the #OnTopic podcast, told the Guardian. “Does it have the potential to be devastating for Trump? Yes. But we don’t know what Mueller has, exactly where he’s going, or how long it will take him to get there.”

Lisa Griffin, a law professor at Duke University, said Trump was under pressure from many sides apart from Mueller, and that recent developments in the New York jurisdiction “are currently the more obvious source of jeopardy for the president”.

“I think the recent developments have revealed clearly that this is not a one-front situation, that the southern district of New York is going to play a very significant role in the future of this presidency,” Griffin said.

The list of legal crises that Trump, his family and associates need to worry about seemed to explode in the last week. Major developments included:

Federal prosecutors investigating Trump’s inaugural committee, a non-profit, for alleged wrongdoing that could include improper foreign contributions, pay-for-play or illegal payments to pop-up firms, the Wall Street Journal reported.

Prosecutors revealing a non-prosecution agreement with the media company AMI, which admitted paying, “in concert with the [Trump] campaign”, the former Playboy model Karen McDougal for her story of an affair with Trump (which Trump denies).

The significant expansion of Trump’s alleged role in the hush payments scheme, for which Cohen was convicted of multiple felonies, with NBC News placing Trump in a meeting with AMI’s chief, David Pecker, to discuss the payments and his campaign (plus a separate conversation which Cohen recorded).

The spy Maria Butina becoming the first Russian to plead guilty to attempting to tamper in the 2016 election. In her plea, she described how she infiltrated the National Rifle Association and the Republican party to try to cultivate “influential Americans” – unnamed, as yet – and the Trump campaign.

Lawyers for the former adviser Michael Flynn filing a sentencing memo touting his cooperation with Mueller in 19 meetings “totaling approximately 62 hours and 45 minutes”. In a heavily redacted document earlier this month, Mueller described Flynn’s extensive cooperation in as-yet secret investigations.

The White House appeared to have moved with some sluggishness this week in response to the tsunami of bad news. On Tuesday a staged confrontation with the Democratic leaders Nancy Pelosi and Chuck Schumer in the Oval Office backfired egregiously. Trump did not show up for work on Wednesday until well into the afternoon, according to NBC News. It was announced that Trump’s chief of staff, who had been fired, would stay on until January – apparently because Trump has been so far unable to find a willing replacement.

Michael Cohen leaves court in New York on Wednesday. Photograph: Shannon Stapleton/Reuters

Trump’s attempts to distance himself from the hush payments scheme, which he had pleaded ignorance of in April, were equally vexed. On Thursday morning he tweeted he was not criminally liable in the scheme because he had trusted his lawyer, Cohen, not to break the law. But on Thursday afternoon Trump told Fox News that Cohen was a minor employee who did “more public relations than law”.

Trump’s current lawyer, Rudy Giuliani, a former federal prosecutor, offered an extraordinary defense, telling the Daily Beast about the campaign finance violations: “Nobody got killed, nobody got robbed. This was not a big crime.”

The number of discrete federal prosecutor’s offices with investigations under way potentially targeting the president continues to grow, minimizing Trump’s ability to simply pull the plug on the Russia investigation by firing the special counsel.

In addition to Mueller and the southern district of New York, the US attorney’s office for the eastern district of New York appears to be involved in the investigation of the inaugural committee, and Butina is being prosecuted by the US attorney in Washington DC, while the eastern district of Virginia is prosecuting another Russian defendant.

Separately, the New York state attorney general is investigating the Trump Foundation and Trump Organization, and separate federal judges in Washington have allowed two cases to move forward alleging that Trump has violated the emoluments clause of the constitution by accepting illegal foreign gifts.

That’s not to mention potential new investigations being instigated by Democrats when they take hold of the House of Representatives in the new year.

Trump’s immediate plan of defense appears to be a retreat to familiar terrain. The president is expected to spend as many as 16 days over the Christmas holidays at his Florida resort Mar-a-Lago, according to a local alert issued by the Federal Aviation Administration, the Palm Beach Post reported on Thursday.

The FAA advisory is scheduled to be lifted on 6 January, three days after the new Congress is sworn in.