But under their system they could order any number of retrials -- with each new trial to be to be confirmed or overturned by their Supreme Court, which can always order another trial.

The court is considering whether to retry her

Even under the system used here in the US, retrials can occur after a conviction is thrown out on appeal.

She was acquitted in her second trial, as are about 50% of defendants in Italy. They scoop up many innocent people in the first level trials and then acquit them in the second. It's very rare for the Supreme Court to completely reverse an acquittal from the Appeals Court.

http://www.huffingtonpost.com/2013/03/26/amanda-knox-double-jeopardy_n_2956566.html

Attorney Joey Jackson told Headline News that, if Italy requests that Knox be extradited, the U.S. could deny the request because American law includes the concept of "double jeopardy," a principal that bars a defendant from being convicted of an offense after they've already been cleared.

"We have principles that are well-founded within our Constitution, one of which is double jeopardy," Jackson said. "So as a result of that, I think it would be highly objectionable for the United States to surrender someone to another country for which justice has already been administered and meted out. So I don't think or anticipate that that would happen."

ABC News also reports that experts don't think an attempt to extradite Knox would be successful.

not guilty, but does not necessarily apply to a conviction overturned at the appellate level. Knox was found guilty by the original trial court, with the conviction overturned at the appellate level and with a new trial finally ordered by the highest court

But if they acquit, then that's it. They don't send it up to yet another court for review.

again for the same offense, the assumption being made in the first case on the subject that, by appealing, a defendant has 'waived' his objection to further prosecution by challenging the original conviction"
Annotation 5 - Fifth Amendment
Reprosecution Following Conviction
Reprosecution After Reversal on Defendant's Appeal

the Italian Court of Cassation set aside the result of the appeal making it as though it had never occured. As such that restored the original guilty verdict making the subject of double jeopardy incidental.

They have already said that should she chose to return to Italy for a new appeal she would be treated as an innocent for that purppse. The new appeal will eventually occur even in her absense. The result of such a new appeal would also be then refered back to the court of cassation.

And the acquittal made complete sense because there was never any reasonable case against her.

jurisdictions follow the ABA standards: