Biological datasets for polythetic classification
I may not be understanding exactly what you are talking about, but it seems to me that nearly any set of classes of interest must be polythetic. Most groups of comparable things differ in some characteristics but also have characteristics in common, and none of those characters is 100% identical with membership in the class.
Some examples off the top of my head:

Biological species / taxonomic groups (classify according to phenotypic characters)
Biological species / taxonomic groups (classify according to molecular sequence e.g. DNA)
Cell types (classify according to cell epitopes)
Cell types (classify according to transcriptional profile)
Ecosystems (classify according to species profile)
Disease state (classify according to any one of many molecular profiles)
Members of population groups (classify according to genetic variation)

etc.