  In the present paper, we study the correspondence and canonicity theory of
modal subordination algebras and their dual Stone space with two relations,
generalizing correspondence results for subordination algebras in
\cite{dR20,dRHaSt20,dRPa21,Sa16}. Due to the fact that the language of modal
subordination algebras involves a binary subordination relation, we will find
it convenient to use the so-called quasi-inequalities and $\Pi_2$-statements.
We use an algorithm to transform (restricted) inductive quasi-inequalities and
(restricted) inductive $\Pi_2$-statements to equivalent first-order
correspondents on the dual Stone spaces with two relations with respect to
arbitrary (resp.\ admissible) valuations.
