Lawyers said the indictment against their client was obtained unjustly and does not allege crimes specific enough to bring before a jury.
They also said a non-prosecution deal that Epstein reached with the federal government in 2008 should shield Maxwell from prosecution.
The agreement sought to protect Epstein and those around him as he agreed to plead guilty to state charges in Florida that forced him to register as a sex offender. Maxwell was not identified by name in the document.
Lawyers for Epstein had planned to argue that the deal with federal prosecutors protected him against sex trafficking charges lodged against him in July 2019 in New York.
Manhattan federal prosecutors maintained they could proceed against Epstein or those who worked for him regardless.
Epstein killed himself at a Manhattan federal prison a month after his arrest.
Maxwell, 59, was arrested last July and has remained jailed on grounds she might flee.
She has pleaded not guilty to charges that she recruited three teenage girls, including a 14-year-old, for Epstein to sexually abuse from 1994 to 1997.
Federal prosecutors declined to comment and will file arguments in response in a few weeks ahead of a scheduled trial in July.
If Maxwell’s lawyers cannot force a dismissal of the charges against her, they also made requests that would reduce the number of charges she faces.
Among the more unusual filings was a claim that the indictment should be thrown out because it was obtained from a grand jury seated outside New York City in White Plains, where the lawyers said black and Hispanic grand jurors would have been under-represented.
They said the coronavirus outbreak was used as an excuse to seat the grand jury outside of New York City when the pandemic was killing thousands of city residents.
In a footnote, they wrote: “The fact that Ms. Maxwell herself is neither Black nor Hispanic does not deprive of her of standing to raise this challenge.”
They said the fact that a Manhattan grand jury convened as early as June 25 showed there was no reason for prosecutors not to wait “other than a publicity-driven desire to arrest Ms. Maxwell on the anniversary of the Epstein indictment”.