All four cases are brought by white-collar staff currently employed by Dyfed CC. The county is unique in that some staff face being relocated or commuting 60 miles to work once the county is split into three unitary authorities.
John Lloyd, staff side secretary for the north and south Wales APT&C provincial council - the body responsible for handling reorganisation appeals - estimated another 150 appeals were being handled locally across Wales.
Grounds for appeal include wanting to be transferred to a unitary post, and wanting the right to compete for one.
The four Dyfed appeals have to be heard within the next three weeks.
Twenty-one employees had originally lodged local appeals against staff transfer plans.