There are now four buildings at Wellington's CentrePort which could be demolished following the 7.8 magnitude earthquake.
The Statistics New Zealand Building is already under investigation for its poor earthquake performance.
Now it has been announced that Shed 35, a vacant cargo store, has sustained serious damage.
The 1915 building is heritage-listed and has been vacant for many years because of its earthquake prone status.
CentrePort chief executive Derek Nind said options for the building include demolition.