Teachers in Angus, Aberdeenshire and Clackmannanshire could join Dundee colleagues in taking strike action over the implementation of new Higher exams.
The Courier revealed in February Dundee teachers could make the move amid fears the new system is being rushed through.
General secretary of the Educational Institute of Scotland (EIS) Larry Flanagan has demanded individual school department heads are allowed to delay, which has been offered to schools by education minister, Mike Russell.
He said those councils that do not offer that option could face the walk-outs.
In a letter sent to the education committee Mr Flanagan alleges 11 local authorities are taking a “unilateral approach”.
The list includes Angus, Aberdeenshire, Clackmannanshire and Dundee.
A spokesman for Aberdeenshire Council said: “There is no unilateral position, quite the opposite.
“The head teacher, working with staff and parents, is best placed to determine the Higher qualifications that will meet the needs of the young people in each school.”
An Angus Council spokesman said its schools are moving to the new Higher “in almost all cases in 2014-15”.
“Decisions are taken jointly by secondary head teachers and senior officers of the council and are always done while considering the best interests of our young people.”
A spokeswoman for Clackmannanshire Council said: “Any subject areas that have causes for concern will be supported towards a resolution that is in the best interest of our pupils.”
A Dundee City Council spokesman said: “Dundee City Council is committed to offering the new Higher across all our secondary schools in 2014-15.
“The education department is working closely with staff and unions and discussions are ongoing about these changes to the exam system.”
Scottish Conservative education spokeswoman Liz Smith has urged the Scottish Government to intervene in the stand-off between the EIS and councils.
She said: “It is head teachers and departmental heads who are best placed to decide when to implement the new exams.”
A spokesman for the Scottish Government said: “Decisions can be made to retain the existing Higher for a year where it is in the professional judgment of the teacher to be in the best interests of their pupils, and agreed in consultation with the school, local authority and parents.
“Local authorities have developed robust procedures to ensure that decisions on whether to use the existing or new higher in 2014-15 are being made in the best interests of young people and in consultation with their parents.”