I can suggest only cladoendesis; see:

http://www.insecta.bio.spbu.ru/z/cladoendesis.htm

There is a book in press "Insect systematics and principles of cladoendesis" (now in Russian only, English version is in progress)

I'd like to add an honourable mention of the work of our sorely missed colleague Peter Hovenkamp (1952-2019), who had been drafting a new approach for representing taxonomic opinions (and the provenance chains between them) using Neo4J graphs.

The idea is very, very cursorily mentioned in this paper 10.3897/BDJ.2.e1125 and in some code samples here: https://gist.github.com/PeterHovenkamp/9684109

The general idea was the taxon concepts would become the topologically emergent properties of graphs that link specimens by way of the expert opinions that connect them as conspecifics.

There is a lot of similar topics just published on a new journal "Megataxa".

https://www.mapress.com/j/mt

You may refer these papers for your question.

Without taxonomy there are not order on Animal and Vegetal Kingdom,because most species are known by owen names and these names are building on rules of systematic and this rules stablish hierarquichal levels, for example a Family can included some Genera and one Genera can to included some species.

You can see the following books (in Spanish)about it:

1.La Taxonomía y la Revolución en las Ciencias Biológicas.Monografía no.3.serie biología.Organización de los Estados Americanos.Programa Regional de Desarrollo Científico y Tecnológico.Washington,D.C.

2.Introducción a la Teoría y Práctica de la Taxonomía Numérica.Monografía no.26.serie biología.Organización de los Estados Americanos.Programa Regional de Desarrollo Científico y Tecnológico.Washington,D.C.