Regional meetings involving principals from schools with teachers belonging to both the ASTI and TUI are to take place today and tomorrow.
The meetings come ahead of next week's planned strike action by members from the Association of Secondary Teachers in Ireland (ASTI) which could potentially see hundreds of schools close over the coming weeks.
About 160 schools are "dual union", including the majority of the country's 97 community and comprehensive schools.
ASTI leaders met officials at the Department of Education yesterday ahead of its planned strike action in protest over pay and conditions.
The talks, aimed at averting industrial action, will resume again on Monday.
The ASTI has planned seven days of strike action, which is due to begin next week.
In addition to strikes between next week and December, ASTI members plan to stop supervision and substitution duties from Monday 7 November.
In an effort to avert this crisis, secondary schools are to advertise for supervisors in national papers.
Parents will also receive application forms in the post.
However, the Department of Education has already said it could take up to nine weeks to get personnel in place.
The Teachers' Union of Ireland has said that advertising for parents to supervise during upcoming strike days at secondary schools is "fraught with difficulty".
Archbishop warns of 'compromised ethos' in catholic schools
The Catholic Archbishop of Dublin has said a pluralist society needs faith-based schools but that Catholic schools have in some cases suffered from a split personality.
Dr Diarmuid Martin warned that if Catholic schools feel that they can continue to be all things to all citizens then they may well end up with a compromised ethos.
Archbishop Martin made his remarks to a conference on faith-based schools in a secular society in Dublin organized by "The Irish Catholic" newspaper.
He told the gathering Catholics need to translate their vision from a language which springs from their faith into one of reason and dialogue, without losing its originality.
He said the faith-based school must be one which fosters critical reflection and the societal conviction on the part of its students.
"As believers," he told his audience, "we have to identify aspects of our faith-language" which are understood and find resonance and attraction "in a more secular world where there is however still a sense of seeking for meaning."
He said a pluralist society needs faith-based schools but that Catholic schools have in some cases "suffered from a split personality".
He warned that if Catholic schools which are also State schools feel that they can continue to be all things to all citizens, then they may well end up with a compromised ethos as they try to fit in with what he called "the scrambled ethos of the student and family mix around them".