Three. (20 points) In the pyramid $S-ABC$, $SA=4, SB \geqslant 7, SC \geqslant 9, AB=5, BC \leqslant 6, AC \leqslant 8$. Try to find the maximum volume of the pyramid $S-ABC$.
Three, let the pyramid $S-ABC$ satisfy the given conditions:
$$
\begin{array}{c}
S A \leqslant 4, S B \geqslant 7, S C \geqslant 9, \\
A B=5, B C \leqslant 6, A C \leqslant 8 .
\end{array}
$$

We estimate the volume of the pyramid using $\triangle A B S$ as the base.
According to the cosine rule, we have
$$
\cos \angle S A B=\frac{A S^{2}+5^{2}-B S^{2}}{2 \times 5 \times A S} \leqslant-\frac{8}{10 \times} \leqslant-\frac{1}{5} .
$$

Since the height of the pyramid does not exceed its slant height, we have
$$
\begin{array}{l}
V_{S A B C} \leqslant \frac{1}{3} \cdot B C \cdot S_{\triangle B A S} \\
=\frac{1}{6} \cdot B C \cdot A B \cdot S A \cdot \sin \angle S A B \leqslant 8 \sqrt{6} .
\end{array}
$$

In fact, $V_{S A B C}=8 \sqrt{6}$ can be achieved. Take $A B=5$, $S A=4, S B=7, C B \perp$ plane $A B S, B C=6$, and verify it.

Therefore, the maximum volume of the pyramid $S-ABC$ is $8 \sqrt{6}$.