The rule, in the Board's words
The State Board of Equalization's page on new construction, at boe.ca.gov (opens in a new tab), says that when construction is completed, "the Assessor must determine the new base year value for that portion of any newly constructed taxable real property." It then says: "The base year value of the remainder of the property, which has not undergone new construction, shall not be changed."
The same page defines new construction to include "any addition to real property, whether land or improvements, including fixtures, since the last lien date." A second story is an addition to the improvements, so it is new construction under that definition.