It follows an objection from a midlands man to the development.
A second appeal is being lodged against plans to redevelop Stephen's Green Shopping Centre in Dublin.
The 'Save St Stephen’s Green' campaign is submitting an appeal to An Coimisiún Pleanála, backed by more than 25,000 signatures online.
It's also planning a protest at the Stephen's Green Centre this Saturday at 1pm.
It comes after a sole Athlone man appealed against the plans on the basis he thought the eight-storey redevelopment would harm the historic character and skyline of the area.
Yusuf Alraqi is one of the campaign organisers and he says Dubliners feel the proposed design would erase the character of the building:
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