OK, so having an episode of old-timers today. What is the proper term for a set of data that collectively constitutes PII? For example, the individual data points alone are not PII, but collectively, provide a picture that is "linkable" to an individual? PII that is derived from the sum of non-PII data.
The term you are looking for is aggregate or combinal data. At what point to you continue adding data where the entire set is now PII. In education, FERPA has a rule that you don't take data sets with a group of less than 10. It prevents derived PII instances.