  A symmetry-based approach for describing shape-coexistence, is presented in
the framework of the interacting boson model of nuclei. It involves a
construction of a number-conserving Hamiltonian which preserves the dynamical
symmetry of selected bands associated with each shape, while breaking the
symmetries in other states. The resulting structure embodies multiple partial
dynamical symmetries. The procedure is applied to prolate-oblate and
spherical-prolate-oblate coexistence, at and slightly away from the critical
points.
