A note on Guo's perturbation result for symmetric nonnegative matrices

In 1997 Guo Wuwen proved that if $(λ_1,λ_2,\dots,λ_n)$ is the spectrum of a nonnegative matrix with Perron eigenvalue $λ_1$ and $λ_2$ real, then $(λ_1+t,λ_2\pm t,λ_3,\dots,λ_n)$ is the spectrum of a nonnegative matrix for every $t\ge 0$. Whether the same holds for symmetric nonnegative matrices has