Let $W = S + cT$, where $|c| \le 1$ is a real constant and where $S$ and $T$ are square matrices containing real numbers from the interval $[0,1]$.
Assume moreover that the all eigenvalues $\lambda$ of $S$ and $T$ satisfy $|\lambda| \le 1$. (Both matrices are right stochastic in that each row sums to one.)
Is it possible to derive an informative bound for the spectral radius of $W$? Besides being right stochastic, the matrices $S$ and $T$ do not have a special structure (e.g. Hermitian, diagonalizable, ...).