  For several evaluations of special values and several relations known only in
$\mathcal{A}_n$-multiple zeta values or $\mathcal{S}_n$-multiple zeta values,
we prove that they are uniformly valid in $\mathcal{F}_n$-multiple zeta values
for both the case where $\mathcal{F}=\mathcal{A}$ and
$\mathcal{F}=\mathcal{S}$. In particular, the Bowman-Bradley type theorem and
sum formulas for $\mathcal{S}_2$-multiple zeta values are proved.
