  We prove a conjecture which was recently formulated by Maia, Montefusco,
Pellacci saying that minimal energy solutions of the saturated nonlinear
Schr\"odinger system \begin{align*}
  - \Delta u + \lambda_1 u &= \frac{\alpha u(\alpha u^2+\beta v^2)}{1+s(\alpha
u^2+\beta v^2)}
  \qquad\text{in }\mathbb{R}^n, \newline
  - \Delta v + \lambda_2 v &= \frac{\beta v(\alpha u^2+\beta v^2)}{1+s(\alpha
u^2+\beta v^2)}\qquad\text{in
  }\mathbb{R}^n \end{align*} are necessarily semitrivial whenever
$\alpha,\beta,\lambda_1,\lambda_2>0$ and
$0<s<\max\{\frac{\alpha}{\lambda_1},\frac{\beta}{\lambda_2}\}$ except for the
symmetric case $\lambda_1=\lambda_2,\alpha=\beta$. Moreover it is shown that
for most parameter samples $\alpha,\beta,\lambda_1,\lambda_2$ there are
infinitely many branches containing seminodal solutions which bifurcate from a
semitrivial solution curve parametrized by $s$.
