The influence of substitution of Fe by Ni or Co on the glass forming ability (GFA) and soft magnetic properties of the Fe71−x
(x = 1–5) and (Fe1−x−y
)71Nb6B23 (x = 0.1–0.2, y = 0.1–0.2) amorphous ribbons was systematically studied. The Ni or Co substitution for Fe enhances the GFA and decreases the thermal stability for Fe–Nb–B–Ni and (Fe, Ni, Co)–Nb–B alloy systems. The alloys with Ni and Co substitution have lower glass transition temperature and wider supercooled liquid region than that with Ni substitution. The (Fe0.7Ni0.1Co0.2)71Nb6B23 alloys achieved the maximum supercooled liquid region of 78 K. The saturation magnetization decreased and the coercivity increased with increasing Ni or Co content. The (Fe0.8Ni0.1Co0.1)71Nb6B23 amorphous ribbons exhibited the best soft magnetic properties with high saturation and low coercivity. The findings of Fe-based multicomponent alloys with large GFA, low cost, and good magnetic properties are encouraging to develop new soft magnetic materials.