The phenomenon of shape coexistence, occurring frequently in the vicinity of nuclear subshell closures, is investigated within a schematic model with protons in two subshells and neutrons in a single shell. The results of this study shed some light on how one should model the phenomenon within the interacting-boson framework and relates to previous phenomenological studies. Our model employs an SO(8${)}_{\ensuremath{\nu}}$\ensuremath{\bigotimes}SO(8${)}_{\mathrm{\ensuremath{\pi}}+}$\ensuremath{\bigotimes}SO(8${)}_{\mathrm{\ensuremath{\pi}}\mathrm{\ensuremath{-}}}$ dynamic symmetry to ensure exact decoupling of an S-D-pair space, thus providing a tight conceptual link with the interacting-boson model. The model has a critical point, namely, below a certain number of valence neutrons the deformed configuration ceases to coexist. This is intriguingly reminiscent of the data.