  We define $Z$-signable correspondence assignments on multigraphs, which
generalize good correspondence assignments as introduced by Kaul and Mudrock.
We introduce an auxiliary digraph that allows us to prove an Alon-Tarsi style
theorem for DP-colorings from $Z$-signable correspondence assignments on
multigraphs, and apply this theorem to obtain three DP-coloring analogs of the
Alon-Tarsi theorem for arbitrary correspondence assignments as corollaries. We
illustrate the use of these corollaries for DP-colorings on a restricted class
of correspondence assignments on toroidal grids.
