  Coupled XY model systems consisting of three-dimensional (3D) systems with
disordered interlayer physics are of significant theoretical interest. We
realize a set of coupled quasi-2D layers of $^{87}$Rb in the presence of
disordered inter-layer coupling. This is achieved with our high bandwidth
arbitrary optical lattice to obviate restrictions on the dimensionality of
disorder with speckle-generated optical fields. We identify phase crossover
regions compatible with the existence of a pair of intermediate Griffiths
phases between a thermal state and the emergence of bulk 3D superfluidity.
