Florida’s no-fault auto insurance system is again on the chopping block in the Legislature, despite industry concerns the proposed change wouldn’t lower premiums as backers contend and could increase lawsuits and health-insurance rates.

The House Insurance & Banking Subcommittee on Tuesday backed a measure (HB 771) that would replace a requirement that motorists carry personal-injury protection coverage — key to the no-fault system — with mandatory bodily injury coverage.