The court met Wednesday to examine the verdict that found Knox and her ex-lover Raffaele Sollecito guilty of killing British student Meredith Kercher in a case rich with sub-texts of drugs, alleged sexual debauchery and police bungling.
Judges will either uphold one or both of the murder convictions, or send the entire case back to the appeal stage – which could eventually see the pair acquitted.
The verdict – which could spark a request for Knox's extradition from the United States – had initially been expected by the end of the day, but court president Gennaro Marasca said a ruling would not come until Friday to allow the prosecution and defence enough time to present their arguments.
Friday's hearing will give the floor to Sollectio's defence lawyer Giulia Bongiorno before the judges retire to consider their ruling.
Sollecito, 30, arrived at the Rome courthouse in the pouring rain, ushering his girlfriend Greta Menegaldo before him through the crush of international media gathered at the entrance.
Knox's lawyer Carlo Dalla Vedova told journalists outside the court he had spoken to the American and she was watching closely and was "worried".
Kercher was found in a pool of blood in a house she shared with Knox in November 2007, half-naked and with her throat slashed. She had been stabbed 47 times in what prosecutors initially claimed was a satanic rite.
Just under a year later, Ivory Coast-born drifter Rudy Guede was jailed for her murder, with the judge in his fast-track trial concluding that he had not acted alone.
In December 2009, Knox and Italian Sollecito were sentenced to 26 and 25 years in prison for their part in the killing in Perugia.
After four years in jail, the pair were acquitted on appeal in 2011 and Knox returned to the United States.
The couple were found guilty again in a shock about-turn in January last year after judges ruled Kercher died after a row with Knox which spiralled out of control.
The Seattle native, 27, who now works as a journalist and is reportedly engaged to a childhood friend, was handed 28 years and six months in prison, while Sollecito was given 25 years and had his passport confiscated.
"We do not expect this to be the last hearing. We hope the court will annul the verdict and send the case back to appeal," Knox's second lawyer Luciano Ghirga told AFP.
He refused to speculate about a possible extradition. Knox has said she will have to be dragged back "kicking and screaming".
Legal experts are divided as to whether an extradition request would succeed with Knox seen by some in the United States as having already been tried twice for the same crime on the basis of unreliable DNA evidence.
DNA evidence crucial
DNA evidence was central to the convictions. Sollecito's DNA was found on Kercher's bra strap but his lawyers claim the sample was contaminated by police incompetence.
Knox's DNA was found mixed with Kercher's blood, but in the bathroom, not the bedroom where she died, and DNA traces on the presumed murder weapon were so small they were dismissed as inconclusive by the defence. Guede's DNA was found on Kercher's body.
Prosecutors say the stab wounds show more than one person was involved, and insist Knox and Sollecito fatally slashed Kercher while Guede held her down and sexually abused her.
The appeals court placed importance on a written confession Knox made under police questioning, in which she said she had been in the house and had heard the murder, but had not taken part.
She also initially accused a local barman of the murder, but later retracted the statements, claiming they had been made under duress.
Knox and Sollecito have provided each other with alibis, claiming they smoked marijuana and slept together at another apartment on the night of the crime.
But Sollecito admitted last year that he could not remember if Knox was present all the time.