SAN FRANCISCO — For the second time, lawyers for Facebook Inc. asked a federal judge on Thursday to sign off on a $20 million settlement in a class action over its “Sponsored Stories” advertising feature.

In August U.S. District Judge Richard Seeborg of San Francisco rejected a proposed deal between Facebook and plaintiffs that provided for $10 million in charitable donations and up to $10 million in attorney fees, but no monetary benefit to class members.