Fife, which joins Aberdeen in rethinking the traditional holiday pattern, says it wants a better deal for pupils, parents and teachers.
The idea is to make each term more "balanced" and, if support emerges from a consultative exercise, the changes could be introduced as early as next year.
The mid-term October break would be extended to two weeks with a one-week holiday in February, as well as the two-week Easter break. The weeks would come from the summer period.
Jim Macgregor, support services manager in Fife's education department, said: "We are keen to build a pattern of school holidays which meets the needs of today's children and their families without affecting standards of education. The proposals we have put forward are suggestions which have come from earlier discussions on school holidays."
The council is to canvas views from schools, school boards, parent-teacher associations, teaching unions and pupil councils.
The holiday shifts being contemplated by Fife and Aberdeen would be contained within the current total of a 190-day year for pupils and 195 days for teachers.
Fife says the new holiday pattern would reflect parental preferences for family holidays and hopes to minimise the tendency of parents to take their children out of school during term time.
Aberdeen agreed last week to toughen its stance on parents who take children out of school for family holidays. Between last August and October, family holidays meant 8,000 daily absences in the city's primary schools and 2,718 in secondary.
John Stodter, Aberdeen's director of education, said: "The discretionary power for headteachers to decide on whether an absence is authorised leads to inconsistency in reporting, while the facility for parents to request permission to remove a child to go on holiday goes beyond what is envisaged in the legislation, in my view."
The preoccupation of Aberdeen and other authorities is that schools have to aim for improvements in attendance as well as attainment, which are being hampered by cumulative absences from school. There is evidence of "learning loss" following even relatively short periods of absence, Mr Stodter says.