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We report the phase transformations under various conditions of manganese-based multiferroic perovskite materials with 6% titanium-doping at the magnetic B site in Sr_1-xBa_xMn_1-yTi_yO_2+d (with d ~ 0.4 – 1). A multiferroic perovskite material of the composition Sr_0.4Ba_0.6Mn_0.94Ti_0.06O_2+d, was studied by in-situ TOF neutron diffraction under oxidizing and reducing conditions. Oxygen partial pressure dependence of the system’s structure at high temperature was investigated using POWGEN at the SNS, ORNL facility. A fully oxygenated precursor of the same composition was subjected to consequent redox annealing cycles from which we observed a reversible sequence of phase transformations. Slow annealing of an oxygen-deficient material (d ~ 0.4), on the other hand, under controlled oxygen partial pressure conditions give evidence for the presence of a miscibility gap with phase separation consisting of two coexisting phases having oxygen stoichiometries d ~ 0.4 and d ~ 1.0. Further, our results shed light on the suppression of the intermediate oxygen ordered states previously observed with the parent SrMnO_2+d material.