To study the effect of alloy composition on phase selection in the CoCrCu_0.1FeMoNi high-entropy alloy (HEA), Mo was partially replaced by Co, Cr, Fe, and Ni. The microstructures and phase selection behaviors of the CoCrCu_0.1FeMoNi HEA system were investigated. Dendritic, inter-dendritic, and eutectic microstructures were observed in the as-solidified HEAs. A simple face centered cubic (FCC) single-phase solid solution was obtained when the molar ratio of Fe, Co, and Ni was increased to 1.7 at the expense of Mo, indicating that Fe, Co, and Ni stabilized the FCC structure. The FCC structure was favored at the atomic radius ratio δ ≤ 2.8, valence electron concentration (VEC) ≥ 8.27, mixing entropy ΔS ≤ 13.037, local lattice distortion parameter α₂ ≤ 0.0051, and ΔS/δ² > 1.7. Mixed FCC + body centered cubic (BCC) structures occurred for 4.1 ≤ δ ≤ 4.3 and 7.71 ≤ VEC ≤ 7.86; FCC or/and BCC + intermetallic (IM) mixtures were favored at 2.8 ≤ δ ≤ 4.1 or δ > 4.3 and 7.39 < VEC ≤ 8.27. The IM phase is favored at electronegativity differences greater than 0.133. However, ΔS, α₂, and ΔS/δ² were inefficient in identifying the (FCC or/and BCC + IM)/(FCC + BCC) transition. Moreover, the mixing enthalpy cannot predict phase structures in this system.