In the 1930s and 1940s, plans were made to demolish the building, and all other buildings on the block on which it is located (which covered an area on Dawson Street, Molesworth St., Kildare St. and the North side of Saint Stephen's Green[?]), to enable the building of a new Dublin City Hall. However the decision of the Irish Government to erect a new Department of Industry and Commerce on a site on the block, on Kildare Street, led to the abandonment of the plans.
For more information on Dublin City Council (of which the Lord Mayor is Chairperson) see:-