We propose a superconducting wire array that realizes a family of quantum Hamiltonians that possess combinatorial gauge symmetry -- a local symmetry where monomial transformations play a central role. This physical system exhibits a rich structure. In the classical limit its ground state consists of two superimposed spin liquids; one is a crystal of small loops containing disordered $U(1)$ degrees of freedom, and the other is a soup of loops of all sizes associated to $\mathbb{Z}_2$ topological… Expand