The world’s biggest retailer hopes to derail history’s biggest private civil-rights case next week by arguing before a federal appellate panel that a massive gender-discrimination lawsuit against Wal-Mart is too big.

The lawsuit accuses Wal-Mart of systematically favoring men over women in pay and promotion. An appeals court ruling that backs turning the case into a class action affecting as many as 1.5 million women not only would put billions of dollars at stake, but also would set up a battle that both sides say would mean a lot for other employers and employees.