The Ecuadorian courts have set damages at $27bn£16.5bnbn).
The State Supreme Court ruled in Briarcliff's favor and set damages at $15 million.
The lower court had set damages at 32 million kronor ($4.5 million).
A judge would decide on its merits, and set damages or devise a formula for them.
The House bill allows states to set damage limits lower than the federal caps, but states could not set higher limits.
If the judge finds that MP3.com willfully violated the law, he could set damages as high as $150,000 per compact disc.
The jury in New York set damages at $8 million in the case of Shirley Boles, 72, of Fort Walton Beach, Fla., who said she developed osteonecrosis of the jaw by taking Fosamax.
Each side will argue its case briefly Tuesday morning at the federal courthouse in Manhattan, and lawyers said the jury might set damages shortly after that.
Robert A. Clifford, the chairman of an American Bar Association task force on terrorism, said the association opposed the use of a grid to set damages because no arbitrary limits should be set on the amount a victim's family might receive.
Several plaintiffs' lawyers said that if a grid were used to set damages, some victims' families would refuse to participate and would instead file lawsuits against the airlines, airline security companies and others.
Judge Kimba M. Wood of United States District Court in Manhattan ruled a year ago that LimeWire had violated copyright, and when the settlement was reached, the case was in trial to set damages.
