Universal elemental homology (UEH) is used to establish homology of thecal plates and elements of the ambulacral system among clades of stemmed echinoderms by placing these structures into a testable hypothesis of homology. Here UEH is used to explore hypotheses of homology in blastoids, coronoids, Lysocystites, hemicosmitoids, and glyptocystitoids. This new approach to analyze homology is particularly powerful in understanding the nature of the thecal plates of blastoids and how they relate to other taxa in a common nomenclatural lexicon. In blastoids, deltoids are interpreted as oral plates that are homologues to oral plates of glyptocystitoids and hemicosmitoids whereas side plates are interpreted to be ambulacral floor plates. Thecal plates are homologous among blastoids, coronoids and Lysocystites but these morphologies cannot be reconciled with plate circlets of glyptocystitoids and hemicosmitoids. A phylogenetic analysis of these taxa presents the origin of blastoids as sister taxon of coronoids within a testable series of homologies.