  We consider a variant of the Seiberg-Witten equations for multiple-spinors.
The moduli space of solutions to our generalized Seiberg-Witten equations in
the setting of K\"ahler surfaces has a direct relation with ASD connections of
holomorphic vector bundle. Also in K\"ahler setting, we construct a numerical
invariant from the equations that detects a notion of $\phi-$stability of
$SU(n)-$holomorphic vector bundles where $\phi$ is some prescribed non-trivial
holomorphic section.
