The spin multiplicity effects on the second hyperpolarizability (gamma) are investigated for a small-size open-shell neutral conjugated model, the C5H7 radical, in the doublet, quartet, and sextet states by using several ab initio molecular orbital and density functional theory methods. The spatial contributions of total, alpha- and beta-electrons to gamma are examined to characterize the spin polarization and electron correlation effects on gamma. It turns out that the second hyperpolarizability increases with the spin multiplicity, suggesting the interest of designing spin-enhanced nonlinear optical (NLO) systems based on open-shell neutral organic compounds, which also present the possibility of spin control of the NLO properties.