The heads of the National Labor Relations Board are planning a restructure of administrative staff at the agency’s roughly 26 regional offices, including demoting employees in certain job classifications nationwide.

The plan would reclassify almost all NLRB administrative professionals as general “program support assistants,” and place those employees into the same grade within the government’s General Schedule pay system, according to a notice from the NLRB Union to members obtained by Bloomberg Law. The move means some of those employees...