By Maggie Taggart
BBC NI education correspondent
The group representing voluntary grammar schools has suggested an interim scheme to break the deadlock over the future of academic selection.
Finding a replacement to the test has proven controversial
It has been welcomed by the education minister, but she does not go as far as accepting it.
The Governing Bodies Association wants the right to choose children who could cope with an academic education.
It also proposes that grammar schools would agree to reject those whom they feel are not suitable.
That could lead to grammar schools having empty places, instead of filling up with those who currently scrape in with low grades in the 11-plus.
The system would use pupil profiles, however, that could be opposed by primary school teachers who write the profiles and who have been concerned about pressure from parents.
Education Minister Caitriona Ruane has welcomed the proposals, but without committing herself to accepting them.
The schools emphasise this would be an interim solution so it could give the assembly breathing space to win agreement on a permanent system.