Apparently, the API method for controlling buildings takes an integer count:
pCity:SetNumRealBuilding(GameInfoTypes["BUILDING_MONUMENT"], 1) (Link.)
This seems to get used with values greater than
1 by mods that change happiness in an AI-compatible way by adding multiple copies of a dummy building into cities, so multiple copies of buildings are supported by the game.
Are there any situations in the base game and official DLC that will cause more than one copy of the same building to become present in a city? Are there any stock buildings that have the "NoLimit" flag set to enable this? The existence of the building doesn't necessarily have to be exposed in the GUI.