Apple faces an $850m damages claim after the company was found guilty in July 2013 of conspiring with five publishers to raise the prices of e-books to compete against Amazon.
This is triple the original amount sought by a number of state attorneys general and consumers pursuing class actions against Apple, according to the International Business Times.
US District Judge Denise Cote, who found Apple guilty of playing a central role in a conspiracy to fix prices, confirmed that the new $840m damages claim will go to court later this year.
However, Apple is still appealing against the 2013 judgement.
The 2013 anti-trust case was brought by the US Department of Justice, which charged Apple with conspiring with publishers to adopt the so-called agency model.
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Switching to the model meant the publishers set the price of e-books directly, effectively ending Amazon’s ability to set its own prices.
The five publishers were originally named as defendants alongside Apple, but later reached settlements.
Penguin settled its case for $75m and Macmillan settled for $26m, while Hachette, HarperCollins and Simon & Schuster created a $69m fund for refunds to consumers.
In addition to appealing against the conspiracy ruling, Apple is calling for the removal of antitrust compliance monitor Michael Bromwich, accusing him of personal bias against the company.
Bromwich was appointed by judge Cote to keep an eye on Apple for two years, but the iPhone maker claims the monitoring is “unprecedented, impermissible, and unconstitutional".
"The court authorised the monitor to exercise authority that is not judicial,” the firm said in an appeals court filing.
On 4 February, an appeals court panel is to hear Apple’s arguments to have the monitoring halted.