  If $L$ is a classical link then the multivariate Alexander quandle, $Q_A(L)$,
is a substructure of the multivariate Alexander module, $M_A(L)$. In the first
paper of this series we showed that if two links $L$ and $L'$ have $Q_A(L)
\cong Q_A(L')$, then after an appropriate re-indexing of the components of $L$
and $L'$, there will be a module isomorphism $M_A(L) \cong M_A(L')$ of a
particular type, which we call a"Crowell equivalence." In the present paper we
show that $Q_A(L)$ (up to quandle isomorphism) is a strictly stronger link
invariant than $M_A(L)$ (up to re-indexing and Crowell equivalence). This
result follows from the fact that $Q_A(L)$ determines the $Q_A$ quandles of all
the sublinks of $L$, up to quandle isomorphisms.
