Some of the schools that are given up by the Catholic Church in the coming years may be run along multi-denominational lines by local Vocational Education Committees.
The VECs already manage five primaries in Leinster.
At Naas Community National School, pupils follow the VEC religion curriculum, Goodness Me Goodness You.
Principal Marianne Henry said: "For most of the time (during the period set aside for religion) the children are taught together, using stories, songs and poems. It is a programme that emphasises diversity.''
Unlike the Educate Together schools, the new VEC schools have some faith formation during school hours.
"The children separate into belief groups for between three and four weeks each year, and that is when there is differentiated teaching.''
At present the Minister for Education is patron of the new primary schools, but patronage is likely to be transferred to the VECs by legislation in the coming years.