Single-phase multiferroics exhibiting simultaneously ferroelectric (FE) and magnetic properties are very attractive for both fundamental research and the advanced technology applications. Such materials are very rare and usually are based on the two-independent structural sublattices. By using the tolerance factor arguments, we have designed and synthesized the unique multiferroic system based on the single Mn-ion. Here we report the synthesis and the x-ray powder diffraction structural studies of the Ba_1-xSr_xMn_1-yTi_yO₃ phase diagram. Compounds with x ~ 0.5 and y = 0 – 0.2 show large FE distortions below ~ 400 K that are identical to the tetragonal distortions of the prototypical nonmagnetic BaTiO₃ but with the much larger distortion size and the temperature hysteresis. Moreover, our compounds are also antiferromagnetic below T_N ~ 200 K due to the presence of magnetic Mn⁴⁺ ions. Extremly strong coupling between FE and magnetism is observed by the very large or complete suppression of FE distortion below T_N, which does not show the temperature hysteresis and can be controlled by the substitution levels x and y. Experiments using hydrostatic pressure show rapid suppression of FE transition while the magnetic T_N increases with pressure as confirmed by magnetic measurements.