  Given a row-finite, source-free, graph of rank k, we extend the definition of
reduction introduced by Eckhardt et al. This constitutes a large step forward
in the extension of the geometric classification of finite directed graph
$C^*$-algebras presented by Eilers et al. to higher-rank graph $C^*$-algebras.
This new move acts as an inverse to delay, directly extends the previous
version, and provides previously undocumented Morita classes of k-graphs. In
pursuit of this extension, we formalize what constitutes a higher-rank graph
move. Specifically, we use this formalization as a bridge between the new
geometric reasoning and the classical category theoretic construction.
