  We present an algebraic procedure for constructing Hamiltonians with several
distinct partial dynamical symmetries (PDSs), of relevance to shape-coexistence
phenomena. The procedure relies on a spectrum generating algebra encompassing
several dynamical symmetry (DS) chains and a coherent state which assigns a
particular shape to each chain. The PDS Hamiltonian maintains the DS
solvability and quantum numbers in selected bands, associated with each shape,
and mixes other states. The procedure is demonstrated for a variety of multiple
quadrupole shapes in the framework of the interacting boson model of nuclei.
