It's definitely not possible with the standard Finder. I seem to remember some app that allows you to either have multiple Docks and/or put it exactly where you want, but can't remember the name of it.
You can use Secrets, among other programs, to position the Dock at the Start, Middle, or End of the side you display it on, in addition to placing it at the top of the screen. That will do what you want.
There are other programs that do it as well, that's just the one I use.