Overwrite files with `docker run`
<p>Maybe I'm missing this when reading the docs, but is there a way to overwrite files on the container's file system when issuing a <code>docker run</code> command?</p>

<p>Something akin to the <code>Dockerfile</code> <code>COPY</code> command? The key desire here is to be able to take a particular <code>Docker image</code>, and spin several of the same image up, but with different configuration files. (I'd prefer to do this with environment variables, but the application that I'm Dockerizing is not partial to that.)</p>