The controversial social media influencers appeared in a federal court in Miami on Monday following their arrest on Saturday over a UK extradition request.
British authorities have brought 38 new charges against the pair, who have repeatedly denied wrongdoing.
Andrew, 39, has been charged with seven further counts of rape and several trafficking and assault offences, while Tristan, 38, is charged with two counts of rape, sexual assault and trafficking offences.
Andrew has also been charged with offences relating to "indecent images of a child and extreme pornography".
The Crown Prosecution Service (CPS) said it had identified four additional alleged victims. It said the 38 additional charges, in addition to 21 existing charges, relate to alleged offences between July 2010 and August 2017.
The brothers have previously denied allegations of sexual abuse and trafficking, claiming that violent and misogynistic statements have been taken out of context or were intended as jokes.
Speaking outside court, Mr McBride suggested the Tates' case "had a lot to do with" Sir Keir Starmer's decision to step down as prime minister and said it was no coincidence that the brothers were arrested after meeting "friends in Washington, DC".
Describing the further charges as "salacious and defamatory", he said: "Some of them are despicable, meritless, heinous and atrocious. They're designed to poison the jury pool, to re-poison public consciousness."
Mr McBride also raised the possibility of US President Donald Trump intervening in the extradition proceedings, arguing "he was elected to fight against this kind of nonsense".
He said the pair "remain positive" after speaking to them on Monday.
Before the hearing, he dismissed the case as a "political witch hunt", calling the charges "filth and slander". On Sunday, Mr McBride said he was confident the extradition request would be denied.
Legal proceedings would take around 60 days, Mr McBride said.
The brothers, normally photographed in tailored suits and stylish fitted shirts, wore tan jail uniforms and handcuffs during the brief hearing.
Magistrate Lauren Louis set another hearing for next Monday.
While a US district judge can consider whether conditions are met for extradition, the ultimate decision falls to Secretary of State Marco Rubio.
The State Department could deny, but it has granted nearly every British request since ratifying a strengthened extradition treaty in 2007.
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It's the latest chapter in the brothers' long-running international legal saga that has spanned the US, Britain and Romania.
The brothers, who are US and British citizens, have built a social media empire promoting wealth, male dominance and misogyny, which has made them among the world's most polarising internet personalities.
Arrested in Romania in 2022, they were accused of participating in schemes to lure women for sexual exploitation, allegations they deny.
In a statement, Karoline Leavitt, the White House press secretary, said Donald Trump would return to an older Air Force One jet for about a month, but insisted the new Boeing 747-8 - a present from Qatar - is "perfectly safe".
Mr Trump had earlier told reporters that the aircraft valued at close to $400m (£298.5m), was being sent to be "maxed out".
It comes after several New York Times journalists were summoned to testify under oath by the US Department of Justice (DOJ) after they reported on security concerns involving the plane.
The newspaper, citing anonymous sources, claimed the new jet lacked some of the advanced features of the older aircraft, including anti-missile capabilities.
Speculation was further fuelled after Mr Trump, who had used the latest plane for the outbound journey, departed a NATO summit in Turkey earlier this month on an older Air Force One jet.
He swapped back onto the new aircraft at Mildenhall, a Royal Air Force base in Suffolk, England, claiming the stop was so US troops could look at the plane.
However, Mr Trump denied that the jet switch was due to security concerns, although he also claimed he has threats against him "all the time" and that he is Iran's "No. 1" target.
'War on the press'
Mr Trump's legal move against the New York Times marked a dramatic escalation of his campaign against the media.
The newspaper said that federal agents had delivered some subpoenas - legal documents ordering someone to appear in court - to the reporters' homes.
It also said that prior to its first story being published, a senior official at the FBI contacted a reporter and editor to ask that the article be held, referencing national security issues.
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The paper said that the FBI official declined to elaborate on the issue, but asked it to disclose its sources for the story, which it said it refused to do.
"The appearance of federal law enforcement agents on the doorstep of news reporters should shock the conscience of any American who believes in the Constitution and the press freedom it protects," a lawyer for the New York Times, David McCraw, said in a statement.
The DOJ said that "to be clear, reporters are not the targets, those leaking classified information are".
The department acknowledged that "there may always be natural tension there", but insisted "we are not going to ignore the law and stop investigating the people who work in the administration and think it's okay to leak classified information impacting national security".
Ofcom said it is investigating an unspecified complaint against the reality TV show.
The reality series, in which single people are matched and married to complete strangers, was investigated by the BBC's Panorama earlier this year.
Its report, broadcast in May, included allegations by two women that they had been raped during production of the show. Another woman alleged a non-consensual sexual act.
All three said the Channel 4 show, made by production company CPL, did not do enough to protect them.
The three men have denied the allegations.
On Monday, an Ofcom spokesperson said it is "investigating a fairness and privacy complaint about Married At First Sight UK".
It is understood the complaint has come from a person or organisation that took part in the show.
Ofcom has also looked into a complaint of unjust or unfair treatment on MAFS, the Press Association understands.
A male MAFS UK cast member was arrested in June on suspicion of rape and bailed, the Metropolitan Police said.
Neither the arrested man nor the alleged victim can be named.
Following the Panorama documentary, chief executive of Ofcom Dame Melanie Dawes said the allegations raised "really serious concerns" and added the regulator is prepared to tighten its guidance around reality shows if necessary.
Channel 4 launched a review into contributor welfare in April, shortly after being contacted by the BBC regarding the accusations featured in Panorama.
The broadcaster's chief executive Priya Dogra has said reports that the show had been cancelled were "wholly inaccurate" and "no decision has been made" regarding the broadcast of the next series.
Ms Dogra said, after watching the programme, she was "deeply sorry" for the distress caused to MAFS UK participants who alleged they were raped and sexually assaulted by their partners.
MPs on the Culture, Media and Sport Committee have written to Channel 4 and Ofcom about their response to allegations in the BBC documentary.
Committee chairwoman Dame Caroline Dinenage said the accusations were "horrifying", adding: "Both Channel 4 and Ofcom, as the broadcasting regulator, have urgent questions to answer."
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Billed as a "bold social experiment", MAFS sees single people agree to "marry" total strangers, after meeting for the first time at their mock weddings.
The "marriages" on the show are not legally binding but the couples go on a "honeymoon" and move in together after their weddings.
The UK version of the reality series, which has been running for 10 seasons, is one of Channel 4's biggest shows, with audience numbers often topping three million.
But, in May, the broadcaster pulled all episodes of the show from its streaming service just hours before the edition of Panorama was aired.
Channel 4 has not yet decided whether to go ahead with the latest season of the show, which has already been filmed.
The 76-year-old, who helped traffic tonnes of cocaine, fentanyl, methamphetamine and other drugs into the US, was arrested in 2024 after he said he was kidnapped in Mexico and flown to Texas.
He then pleaded guilty to drug trafficking charges in August last year, after prosecutors said they would not seek the death penalty.
Speaking through a Spanish-language interpreter at the time, he apologised "to everyone who has suffered or been affected by my actions".
US District Judge Brian Cogan handed down the sentence at a hearing in Brooklyn federal court on Monday.
Along with a life sentence, he also faces $15bn (£11.2bn) in financial penalties.
Prosecutors said that Zambada ordered torture and plotted murders as he and co-founder Joaquin 'El Chapo' Guzman - whose son Joaquin Guzman Lopez was arrested with Zambada - grew the Sinaloa cartel into the world's largest drug trafficking organisation.
Sky's chief correspondent Stuart Ramsay witnessed production at a fentanyl lab run by the Sinaloa cartel in 2023 - where he saw how gang members then transported the drug by boat to a "stash house" ready for shipment to the US.
Prosecutors: Zambada sent 'staggering' amounts of drugs
Prosecutors added in a sentencing memo that Zambada "was one of the most - if not the most - prolific and powerful narcotraffickers in the world", adding "it would be difficult to overstate the magnitude" of his crimes and the scale of the "corruption, violence, and other harm he spread".
Federal authorities said in 2023 that the cartel was sending "staggering" amounts of fentanyl to the US, where the opioid kills thousands every year.
In 2023, at least three people were killed in retaliatory violence that Zambada directed after a large cache of fentanyl pills, methamphetamine and cocaine was stolen from the cartel, prosecutors added.
Months before Zambada's arrest, prosecutors also said that he ordered the murder of his nephew Eliseo Imperial Castro, also known as 'Cheyo Antrax,' after learning that Castro was claiming to be collecting debts for Zambada and pocketing the money without his permission.
After his and Lopez's arrests in 2024, violent clashes broke out in Culiacan between factions of the Sinaloa cartel. At least 12 people were killed.
Cartel violence broke out in February
According to the Reuters news agency, Zambada's lawyer Frank Perez said in a 6 July court filing that his client was fully aware he would receive a life sentence when he decided to accept responsibility for his crimes.
Mr Perez asked Judge Cogan to recommend to the Bureau of Prisons that the elderly Zambada be placed in a facility where he would receive adequate medical care.
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It comes after violence broke out in February after the killing of 'El Mencho' Nemesio Ruben Oseguera Cervantes, the leader of the Jalisco New Generation Cartel.
The 59-year-old was originally from the western state of Michoacan and had been heavily involved in drug trafficking since the 1990s.
He previously spent almost three years in a US prison after being convicted in 1994 of conspiracy to distribute heroin by a court in California.
The ruling, which applies for 14 days, was handed down by a US district judge ahead of a hearing in August.
That is set to determine whether the $110bn (£81.4bn) deal should be paused pending the outcome of the lawsuit brought by the 12 states involved, led by California.
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They argue the merger - mainly aimed at creating a bigger rival to the likes of Netflix - would substantially weaken competition in the US market, driving up prices for consumers and costing jobs.
The opposition is particularly fierce in Hollywood. Movie industry interest groups claim the deal would threaten the very future of cinema as it would bring together two of its five major studios.
The UK government has also outlined concerns.
The companies control UK-based TV channels, including Channel 5, TNT Sports, Cartoon Network, Nickelodeon, and CNN International, as well as the Paramount+ and HBO Max streaming services.
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Neither Paramount or WBD were yet to comment on the US ruling, which was handed down at the Oakland federal court in California.
The state's attorney general, Rob Bonta, said in a statement: "This is a critical first win in our case to ensure this megamerger never sees the light of day.
"History tells the tale of what happens when a few people have great power over markets that are central to Americans' lives: fewer opportunities for more people, worse products and services for all people."
The lawsuit could take many months to reach a conclusion - something that will worry Paramount.
Under the terms of its deal, it is obliged to pay Warner Bros shareholders a 25 cents-per-share fee for each calendar day the merger is delayed beyond 30 September.
It amounts to a bill of around $7m a day.