The Department of Education says 11 out of 42 schools built by Western Building Systems (WBS) can re-open in full without any works needed.
It says structural assessments of all 42 of the schools were completed on Tuesday.
In some cases, further on-site inspections were also required on Wednesday.
Eleven schools have been cleared to open in full without further intervention.
Source: Department of Education and Skills
A further 14 have been cleared to open in full - following external intervention in the form of a fence around the building, and protective decking.
Source: Department of Education and Skills
In three schools, the ground floor will be cleared to open following the implementation of internal engineering solutions and external interventions.
Source: Department of Education and Skills
A further 13 schools are subject to ongoing structural assessment and analysis - while one school building is to remain closed (Phase 1 of Ardgillan Community College).
Source: Department of Education and Skills
Education Minister Joe McHugh says: "The outcomes of further structural assessments which we have received today are important in providing clarity to school authorities, students and parents.
"The advice I have received is that no other building has presented the same severity of structural issues as those identified in Phase 1 of Ardgillan Community College, which was built in 2009."
Contractors have commenced work on-site at five schools previously confirmed as needing internal and/or external interventions.
While teams are also moving to implement necessary external interventions at other schools.
The department says the target is to have this work completed "in the coming days."
An interim accommodation team has also been working with the principals of Tyrrelstown ETNS, St Luke’s National School and Gaelscoil Eiscir Riada, Lucan over recent days to confirm accommodation for classes which will be moved temporarily.
The department says off-site arrangements have been confirmed in principle, and more information will be issued from the schools shortly.
In a response, Western Building Systems says: "No details of the assessments have been shared with us.
"We do not know what any conclusions reached at this point are based on.
"So far, we have been invited to meet with the department's inspectors and officials at 13 of the 42 schools.
"We had insufficient time on site to make structural evaluations."
"We wish to reiterate once more our recognition of the impact this has had on pupils, parents and teachers at the schools involved.
"While it remains unclear as to why and how we have reached this point, we are not walking away.
"We honour our contracts. We continue to engage with the department and remain keen to meet the minister."
