But if it agrees with prosecutors that the appellate court erred — for instance, by not allowing sufficient forensic evidence tests, as Riello contended in court Monday — it throws out the acquittals.
It would then order a new appeals trial. In that case, that trial would be held by an appellate court in Florence, since the smaller town of Perugia only has one appellate court and it cannot hear the same case again.
Should a new trial be ordered, Italian law cannot compel Knox to return. The appellate court hearing the case could declare her in contempt of court but that carries no additional penalties.
It is unclear what would happen if she was convicted in a new appeals trial.
"If the court orders another trial, if she is convicted at that trial and if the conviction is upheld by the highest court, then Italy could seek her extradition," Knox's lawyer Carlo Dalla Vedova said.
Italy is not obliged to seek her extradition but it could decide to do so. It would then be up to the United States to decide if it honors the request. U.S. and Italian authorities could also come to a deal that would keep Knox in the United States.
Riello, the prosecutor general, argued before the court that there were ample reasons "not to bring down the curtain on the case."
Riello contended the appellate court was too dismissive in casting aside DNA evidence that led to the conviction in the lower court, arguing that another trial could make way for more definitive testing.
An attorney for Kercher family members also argued for a new trial. The lawyer, Francesco Maresca, contended that the appellate court tried to have it both ways by saying that it didn't have the scientific expertise to decide the worth of forensic evidence but also deciding which tests to order.
The Kercher family didn't attend Monday's hearing.
Defense attorneys said they were confident the acquittals would be upheld.
"We know Raffaele Sollecito is innocent," said his attorney, Giulia Bongiorno, who called the entire case "an absurd judicial process."
Before the court, Bongiorno argued there was an "unending series of errors by scientific police" in how they handled evidence in the case, including the fact that the crime scene had been disturbed "and possibly contaminated" during the investigation.
Bongiorno noted that a key piece of evidence - a clasp from Kercher's bra -- had been found 1 meter (yard) away from its original position in the bedroom when police forensic experts had gone back to the crime scene 47 days after their original inspection.
A young man from Ivory Coast, Rudy Guede, was convicted of the slaying in a separate proceeding and is serving a 16-year sentence. Kercher's family has resisted theories that Guede acted alone.
The same court also heard arguments in Knox's appeal of her slander conviction for having accused, after police interrogation, a local pub owner of carrying out the killing. The man was held for two weeks based on her allegations, but was then released for lack of evidence.
Riello argued that conviction should stand because "you cannot drag in an innocent person while exercising your right to a defense."
Knox's lawyer Dalla Vedova said the slander verdict should be thrown out because she was questioned without a lawyer even though police essentially treated Knox as a suspect in their 14 hour interrogation session.
"The girl was confused, worn out," her lawyer told the court. Dalla Vedova added that while Knox was alone, 36 investigators signed the interrogation sheet.
Because of time served in prison before the appeals level acquittals, Knox didn't have to serve any time for the slander conviction.
Associated Press writer Chris Grygiel contributed from Seattle.