The suit filed Monday by Matt and Melissa Crusan of Oklahoma seeks to represent the more than 3,000 passengers who were on the Carnival Triumph when the fire broke out on Feb. 10.
A judge must approve the motion to grant class-action status. Carnival requires all lawsuits to be filed in Miami, where the liner is based.
Texas resident Cassie Terry was the first to sue the company, filing a lawsuit less than 24 hours after the boat docked.
Maritime attorneys say it's difficult to win such cases unless the plaintiffs can show actual injury or illness.
Carnival has said it won't comment on Triumph lawsuits.