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The crystal structure of Ca₃Co₂O₆ is constructed from relatively isolated chains of Co ions oriented along the c direction. Strong intrachain magnetic exchange interactions and weak interchain coupling lead to a quasi-one-dimensional ferromagnetic ground state. Chemical substitution studies show that Co and Mn ions alternate along the chains in the system Ca₃Co_2-xMn_xO₆ and that the magnetic structure is tuned from ferromagnetic to antiferromagnetic. Symmetry breaking through exchange striction also leads to multiferroic states in the vicinity of x = 1. Such a highly complex environment is expected to produce a rich temperature vs. manganese concentration phase diagram. In this study, polycrystalline samples in the system Ca₃Co_2-xMn_xO₆ were synthesized via a solid state reaction in the range 0 ≤ x ≤ 1; these samples were studied with measurements of magnetic susceptibility and heat capacity. Using these results, we constructed a temperature-Mn concentration phase diagram.