Objective overall resemblance

What is it for y to be objectively qualitatively overall at least as similar to x as z is? This paper defends a version of the following answer: it is for y to be at least as similar to x as z is in every qualitative respect. On the version defended in this paper, this analysis arguably entails that it is possible for some things to objectively qualitatively resemble each other more than they do other things. However, it also arguably entails that, given how the world contingently is, many things (if not all things) are incomparable in objective qualitative resemblance, where y and z are so incomparable to x iff: (i) it is not the case that y is at least as objectively qualitatively similar to x as z is, and (ii) it is not the case that z is at least as objectively qualitatively similar to x as y is.