A glassy phase is formed over the whole composition range for melt-spun (Fe_1−xNi_x)₇₉B₁₂P₅Si₃C₁ with x = 0; 0.2; 0.4; 0.5; 0.6 alloy ribbons and these glassy ribbons exhibit good bending plasticity. The Ni-containing glassy alloys show glass transition, followed by a supercooled liquid (SCL) region and then multistage crystallization for the alloys with x = 0.5 and 0.6 (hereafter 0.5Ni and 0.6Ni alloys). The 0.5Ni glassy alloy exhibits the largest SCL region of 43 K and good soft magnetic properties even in as-spun state, i.e., low coercive force of 4.8 A/m, effective permeability of 7400 at 1 kHz and saturation magnetization of 0.80 T. The bending plasticity remains unchanged in the wide annealing temperature range below T_g. The crystallization proceeds in the processes of glassy (G) → bcc(α)Fe(Si) + Fe₃B for the 0–0.2 Ni alloys, G → fcc(γ)(Fe,Ni) + Fe₃(B,C) + Fe₃Ni₃(B,C) for the 0.4Ni alloy and G → G’ + γ(Fe,Ni) → γ(Fe,Ni) + Ni₅P₂ + Fe₄P + Fe₃Ni₃(B,C) for the 0.5Ni and 0.6Ni alloys. Analyses of crystallization reaction in isochronal and isothermal conditions were performed via Kissinger and JMAK models and the activation energy for crystallization is much larger for the 0.5Ni glassy alloy. The appearance of the largest SCL region as well as the highest activation energy for the 0.5Ni alloy is due to the necessity of the simultaneous decomposition to the four crystalline phases. The better magnetic softness for the 0.5Ni alloy is presumably due to the development of medium-range ordered atomic configurations which enable the appearances of the largest SCL region as well as the lower internal stress state. The combination of useful properties for the 0.5Ni glassy alloy is promising for useful soft magnetic materials with mass production ability.