Four talcum powder suits against Johnson & Johnson are set to proceed this month to trial in the New York City Asbestos Litigation court, where plaintiffs attorneys may be able to wield a formidable weapon in the threat of punitive damages, a remedy that had been unavailable for more than two decades, but to which the door was opened last year.

Johnson & Johnson has had mixed success around the country in court fights with plaintiffs who say that using the company’s baby powder caused cancer.