Acho que o recurso que você está procurando é chamado de compartilhamento de conexão. Adicione isto ao seu arquivo $HOME/.ssh/config
:
ControlMaster auto
ControlPath /tmp/ssh_mux_%h_%p_%r
excerto # 1 de SSH pode fazer isso? Dicas de produtividade para trabalhar com servidores remotos
Fortunately OpenSSH has a feature which makes it much snappier to get another terminal on a server you’re already connected to: connection sharing.
trecho # 2
Shared connections aren’t just a boon with multiple terminal windows; they also make copying files to and from remote servers a breeze. If you SSH to a server and then use the scp command to copy a file to it, scp will make use of your existing SSH connection ‒ ... Connections are also shared with rsync, git, and any other command which uses SSH for connection.