Andema's directors are listed as Sydney residents John Ramage and Brian Nicholls and New Zealand resident Bret Jackson.
They want the original approval for a two-storey office, entertainment, dining and retail space extended, saying the proposed scale and form of the development is suitable for the area.
Court documents lodged on their behalf say the new building is "consistent with long standing community expectations" for the site.
The Friendly Grocer store in Peregian before it closed its doors.
"The proposed development responds to and protects the natural beach experience which provides a safe public area for aesthetic enjoyment and recreational and social interaction," the documents say.