Quantum spin liquids are highly entangled magnetic states with exotic properties. The S= 1/2 square-lattice Heisenberg model is one of the foundational models in frustrated magnetism with a predicted, but never observed, quantum spin liquid state. Isostructural double perovskites Sr2CuTeO6and Sr2CuWO6are physical realizations of this model but have distinctly different types of magnetic order and interactions due to a d10/d0effect. Long-range magnetic order is suppressed in the solid solution Sr2CuTe1–xWxO6in a wide region of x= 0.05–0.6, where the ground state has been proposed to be a disorder-induced spin liquid. Here, we present a comprehensive neutron scattering study of this system. We show using polarized neutron scattering that the spin liquid-like x= 0.2 and x= 0.5 samples have distinctly different local spin correlations, which suggests that they have different ground states. Low-temperature neutron diffraction measurements of the magnetically ordered W-rich samples reveal magnetic phase separation, which suggests that the previously ignored interlayer coupling between the square planes plays a role in the suppression of magnetic order at x≈ 0.6. These results highlight the complex magnetism of Sr2CuTe1–xWxO6and hint at a new quantum critical point between 0.2 < x< 0.4.