The generic properties are scrutinized in Mn spinels with an immiscibility induced by a Jahn-Teller distortion through the CoFe(2-x)Mn(x)O(4) system. The x-ray diffraction experiment reveals that the immiscibility occurs at 1.1<x<2.0 and the relevant kinetics becomes faster with x. The temperature of the Jahn-Teller transition, which accompanies a sharp resistivity anomaly and matches the immiscibility gap boundary, increases with increasing x. The evolution of the magnetic and structural properties with various thermal treatments is studied carefully in this paper. Based on our comprehensive results, we have constructed a phase diagram of CoFe(2-x)Mn(x)O(4).