To upgrade Basements beyond level 4, Tunnel Excavation must be researched at the Foundry. This also allows you to build Basements (and Towers) closer to each other. With no ranks of Tunnel Excavation, Basements must be radius 6 away from all other existing basements. This is relaxed by 1 radius per rank of Tunnel Excavation to a minimum of radius 3.
When Attic Storage is researched it increases the city's overall resource storage capacity by a percentage of all the Basements capacities.
Up until level 4 a Basement will only protect wood and crop, but from level 5 it will protect gold, and beginning at level 8 it will protect iron.
Later on in the game, one of the main uses of Basements is to increase the storage capacity of your city. In combination with the technology Attic Storage, Basements can provide a big boost to the maximum amount of resources you can have, which becomes important later on when building upgrades and certain technologies begin to cost over 10,000 wood/crop.
Basements can construct a Temporary Basement (6 hour or 12 hour) in order to protect even more resources. The temporary basement's level will equal the level of the basement that constructed it.
All structure and unit stats, cost to upgrade per level, and other abilities can be seen on the Official Database Entry
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