We have grown single-crystal samples of Co substituted CaFe2As2 using an FeAs flux and systematically studied the effects of annealing/quenching temperature on the physical properties of these samples. Whereas the as-grown samples (quenched from 960 degrees C) all enter the collapsed tetragonal phase upon cooling, annealing/quenching temperatures between 350 and 800 degrees C can be used to tune the system to low-temperature antiferromagnetic/orthorhomic or superconducting states as well. The progression of the transition temperature versus annealing/quenching temperature (T-T-anneal) phase diagrams with increasing Co concentration shows that, by substituting Co, the antiferromagnetic/orthorhombic and the collapsed tetragonal phase lines are separated and bulk superconductivity is revealed. We established a 3D phase diagram with Co concentration and annealing/quenching temperature as two independent control parameters. At ambient pressure, for modest x and T-anneal values, the Ca(Fe1-xCox)(2)As-2 system offers ready access to the salient low-temperature states associated with Fe-based superconductors: antiferromagnetic/orthorhombic, superconducting, and nonmagnetic/collapsed tetragonal.