The metazoan last common ancestor probably had minimally epithelial and mesenchymal cells. One or both cell types are likely to have had the capacity to self-renew and transdifferentiate (i.e. act as stem cells). They could convert into each other via epithelial-mesenchyme and mesenchyme-epithelial transitions. Using the single-cell RNA-Seq technique CEL-Seq, here we assess the transcriptomes of pinacocytes, choanocytes and archeocytes from the sponge Amphimedon queenslandica. Pinacocytes comprise external and internal epithelial-like layers, choanocytes form internal ciliated chambers that function in feeding and are part of the internal epithelium, and archeocytes are amoebocytic mesenchyme cells. Choanocytes and archeocytes also act as stem cells, with the latter giving rise to most sponge cell types. Principle component analysis distinguishes these three cell type transcriptomes, with pinacocytes enriched in genes involved in cell adhesion, cell-cell signaling, cell surface receptors - including sensory rhodopsin-like GPCRs - and internal signal transduction (e.g. GPCR signaling pathway, MAPK cascade) consistent sensory epithelia. Genes significantly upregulated in choanocytes are enriched in metabolic and signaling (e.g. Notch) pathways, suggesting a role in feeding and intercellular communication; choanocytes have a greater enrichment in metazoan-specific and novel genes. Many genes upregulated in archeocytes are associated with cell cycle regulation, mitosis, transcription, translation and RNA processing, suggesting these cells are poised to either divide or change expression profiles. Archeocytes also have the most divergent transcriptomes, consistent with these pluripotent stem cells being in a range of cell states. With gene expression in Amphimedon cells being akin to cognate eumetazoan epithelial, mesenchymal and stem cells, we infer that these cell types were part of the crown metazoan body plan that gave rise to extant sponges and eumetazoans.