The attractive/repulsive relationship between superconductivity and magnetic ordering has fascinated the condensed matter physics community for a century. In the early days, magnetic impurities doped into a superconductor were found to quickly suppress superconductivity. Later, a variety of systems, such as cuprates, heavy fermions, and Fe pnictides, showed superconductivity in a narrow region near the border to antiferromagnetism (AFM) as a function of pressure or doping. However, the coexistence of superconductivity and ferromagnetic (FM) or AFM ordering is found in a few compounds [RRh4B4 (R = Nd, Sm, Tm, Er), R'Mo6X8 (R' = Tb, Dy, Er, Ho, and X = S, Se), UMGe (M = Ge, Rh, Co), CeCoIn5, EuFe2(As(1-x)P(x))2, etc.], providing evidence for their compatibility. Here, we present a third situation, where superconductivity coexists with FM and near the border of AFM in Fe(1-x)Pd(x)Te. The doping of Pd for Fe gradually suppresses the first-order AFM ordering at temperature T(N/S), and turns into short-range AFM correlation with a characteristic peak in magnetic susceptibility at T'(N). Superconductivity sets in when T'(N) reaches zero. However, there is a gigantic ferromagnetic dome imposed in the superconducting-AFM (short-range) cross-over regime. Such a system is ideal for studying the interplay between superconductivity and two types of magnetic (FM and AFM) interactions.