There are no virtual consoles over an SSH connection, you just get the one terminal per connection. It sounds like screen may do what you're looking for, though:
Screen is best described as a terminal multiplexer. Using it, you can run any number of console-based applications--interactive command shells, curses-based applications, text editors, etc.--within a single terminal. The desire to do this is what gets most people hooked on screen. I used to start a half-dozen terminal emulators when I logged into my machine: I wanted one to read my email, one to edit my code, one to compile my code, one for my newsreader, one for a shell into my web host, and so on. Now I start one terminal emulator, and run screen in it. Problem solved.
The other main cool feature of screen is its ability to decouple the terminal emulator from the running programs. This means that you can use screen to keep programs running after you accidentally close the terminal emulator, or even after you log out, and later resume right where you were. It means that the idea of a "session" in which you are running a number of console programs is a free-floating entity that you can bind to any terminal anywhere, or no terminal at all if you want.