Let $G$ be a $k$-regular directed graph, that is, a directed graph such that each vertex has $k$ edges going in and $k$ edges going out of it, and suppose further that $G$ has no loops. We can associate a non-directed graph $G'$ to it by ignoring the directions and eliminating double edges. Then $G'$ is a graph with degrees between $k$ (if all the in and out edges collapse to the same) and $2k$ (the other extreme case).
Question: Is there a way to add edges to $G'$ to make it $k'$-regular, for some $k'(k)$ independent of the number of vertices? Clearly $k' \geq 2k$, but even something larger would work.