When working with EMACS over SSH, is there any way to spawn a new frame of the same emacs session on a different terminal?

In my use case, I have screen running, so I have multiple terminals, and can recover which pseudo terminal they're attached to with pts. Suppose I have two "windows" (in GNU screen parlance). The first one is attached to /dev/pts/12 and the second one is attached to /dev/pts/13. I launch emacs on the first window. Is there any way for me to start a new frame of the same session on the second window?

I've been playing with passing arguments to make-frame but it seems that the usage that allows me to specify a terminal requires that a terminal object already exists, and I can't see any way to create a new terminal object.