If you're in SSH you're executing commands on the remote machine. What you're suggesting would require a subset of commands to run on your machine, and a subset

If you're in SSH you're executing commands on the remote machine. What you're suggesting would require a subset of commands to run on your machine, and a subset of commands to run on the remote machine. As everyone else suggests, just use scp. You can always tunnel into your own computer from the remote machine to fetch any files you need.