East Dunbartonshire is bidding to pilot one of two new community schools in a school cluster which takes three-quarters of its pupils from Glasgow.
Education authorities want to create a "one-door" approach, housing a number of services under one roof in 64 new community schools which are planned within the next three years.
In the Bishopbriggs area, a quarter of the pupils at Auchinairn primary and half of those at Thomas Muir High come from the adjacent Glasgow housing schemes of Barmulloch and Balornock as well as from nearby Springburn.
At Auchinairn, 23 per cent of pupils are on free meals and 33 per cent are eligible for clothing and footwear grants. The figures for Thomas Muir are 29 per cent and 46 per cent.
John Simmons, head of educational support services in East Dunbartonshire, said problems of inter-agency liaison persisted although Greater Glasgow Health Board covered both councils.
"If we can come up with a simplified and effective system of co-operation between the education, social work and health agencies," Mr Simmons said, "it could be a model of good practice for other areas of the authority such as Bearsden, where we also attract large numbers of children from Glasgow."
East Dunbartonshire is requesting pound;400,000 a year in Scottish Office funding over the next three years for its two new community school projects, backing it with around pound;150,000 a year from the council and health board.