The program of compiling Ramsey classes that are expansions of the various classes of directed graphs has recently been completed.

For most cases, expanding by arbitrary linear orders fails to be a Ramsey class.

This presents the natural question of what exactly are the Ramsey classes that are expansions of the various classes of directed graphs with arbitrary linear orders.

We provide those expansions as well as answering the dynamical questions of amenability of their respective automorphism groups (of their Fraisse limits).