We can reuse an already connected SSH session to make additional ssh sessions on the same remote machine.

To do this, add the following entries to ~/.ssh/config

host *
    controlmaster auto
    controlpath /tmp/ssh-%r@%h:%p

What this does is set a 'master control' socket when you make an SSH connection. The socket is named based on the 'controlpath' setting (%r = username, %h = hostname, %p = port).

This master socket is used for each successive connection after the first, as long as one connection still exists. That is, if I connect via "ssh myuser@myhost.com", a socket named /tmp/ssh-myuser@myhost.com:22 is created. If I then ssh again to the same host, the socket is found and the remote ssh session is told to spawn a new shell. This shell does not require a login, and spawns immediately, as you're already logged in.