Amid problems in Florida’s property-insurance market, a Senate committee backed a controversial proposal that could lead to many policyholders picking up more of the tab for roof damage and limit attorney fees in insurance disputes.

The Senate Banking and Insurance Committee approved a bill (SB 76) filed after regulators last year signed off on dozens of double-digit rate increases for private insurers and as the state-backed Citizens Property Insurance Corp. has seen a flood of new customers.