Biological systematics, exploring the structure of taxonomic diversity (TD), needs a proper conceptualization that would (a) make it complying with certain universal criteria of scientificity and (b) take into account specificity of its studied object. This article outlines a possible conceptual framework for this natural science discipline based on the ideas of contemporary conceptualism. One of the most fundamental of them includes a concept of cognitive situation shaped by three interrelated basic components—ontic, epistemic, and subjective. Its core position is taken by a taxonomic theory (TT) being a conceptual construct resulted from a “summative” effect of all three components and designed for studying TD. The general TT is shown to be composed by a hierarchically arranged array of partial TTs of various levels of generality, and this construct serves as a conceptual justification of taxonomic pluralism. Several kinds of partial TTs are suggested to recognise, viz., ontology- and epistemology-oriented, aspect- and object-based, etc. The aspect-based TTs are of special importance as the conceptual foundations of particular research programs in systematics. The object-based partial TTs are shown to be implemented by concepts of species and homology. A large-scale relation between taxonomic theory and nomenclature is briefly considered.