Spin-triplet superconductivity in Sr 2RuO 4 has attracted enormous interest. Like other unconventional superconductors, superconductivity in Sr 2RuO 4 is in close proximity to magnetic instability. Undoped Sr 2RuO 4 exhibits incommensurate antiferromagnetic (AFM) fluctuations, which can evolve into static, short-range AFM order via Ti doping. Moreover, weak ferromagnetic (FM) coupling in Sr 2RuO 4 has also been suggested by NMR/neutron scattering experiments and studies on Ca 2−xSr xRuO 4 and Sr 2−yLa yRuO 4, implying orbital dependent magnetism. We report bulk static, short-range FM order in Sr 2RuO 4 triggered by <2% Co doping, showing superconductivity in Sr 2RuO 4 is much closer to FM instability than previously reported in Ca 2−xSr xRuO 4. We also find Mn doping can effectively establish incommensurate AFM order, with T N ~ 50 K for 3% Mn doping. These new results place Sr 2RuO 4 in a unique situation where superconductivity lies directly on the borderline of two distinct magnetic states, highlighting the important role of competing magnetic fluctuations in determining superconducting properties of Sr 2RuO 4.