The full Judiciary Committee planned to take up the bill Tuesday afternoon.
The bill would let voters decide whether to change the state Constitution and eliminate elections for the education superintendent, secretary of state, agriculture commissioner, adjutant general and comptroller general.
The bill also would shift or eliminate some state agencies.
One plan discussed would have put the Department of Health and Environmental Control's health division under a new Department of Health Services, which would include the Mental Health and the Disabilities and Special Needs departments.
The DHEC board last week voted against restructuring the department, sending a message to the Legislature and governor it should keep the agency intact.
The subcommittee approved an amendment Tuesday that requires DHEC to coordinate with the Department of Health and Human Services and report annually to the General Assembly on that effort.