As to the possibility of (mapping to/ significantly correlating with) classical (say: morphological, phenomenological, … ) taxonomy and contemporary taxonomy :

for the ‚classical‘ way and corresponding criticism one may select the historical struggle between William Whewell and John Stuart Mill concerning the question, on whether ‚natural groups are given by type, not by definition‘. I deal with this shortly in fn. 2 and in section 3.2 of my recent ‘note on sorites series‘ (references there).

For a contemporary taxonomy account, there seems a lot of work been done in the ‘homeostasis‘ way, see e.g. Richard Boyd ‚Homeostasis, Higher Taxa, and Monophyly‘ [ Philosophy of Science , Vol. 77] , and more references to this discussion there.

On whether this rather recent development already settles Your question, is beyond my expertise, but perhaps have a look on it.

Kind regards

Thanks Friedrich. I will try to get hold of these papers.

found the Boyd paper on JSTOR, details see below.

kind regards

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Homeostasis, Higher Taxa, and Monophyly

Author(s): Richard Boyd

Source: Philosophy of Science , Vol. 77, No. 5 (December 2010), pp. 686-701

Published by: The University of Chicago Press on behalf of the Philosophy of Science

Association

Stable URL: https://www.jstor.org/stable/10.1086/656551

Only today the following (critical overview of taxonomy accounts) paper was uploaded to philarchive (open access), consider having a look on it

"Classification, Kinds, Taxonomic Stability, and Conceptual Change"

Jaipreet Mattu & Jacqueline Anne Sullivan ( University of Western Ontario )

https://philarchive.org/rec/MATCKT