In search of a quantum phase transition between the two-dimensional (2D) ferromagnetism of CaCo2−yAs2 and stripe-type antiferromagnetism in SrCo2 As2, we instead find evidence for 1D magnetic frustration between magnetic square Co layers. We present neutron-diffraction data for Ca1−x Srx Co2−y As2 that reveal a sequence of x -dependent magnetic transitions which involve different stacking of 2 D ferromagnetically aligned layers with different magnetic anisotropy. We explain the x-dependent changes to the magnetic order by utilizing classical analytical calculations of a 1D Heisenberg model where single-ion magnetic anisotropy and frustration of antiferromagnetic nearest- and next-nearest-layer exchange interactions are all composition dependent.