You could take down the web server and configure a SSH server to use a custom port, 80 or 443. But you can only have one server listening on a given port. So while you've got your SSH going, you'd have to do without http or https.
I've seen CGI-like applications that mimic the shell by taking command line arguments in a form field and excecuting them on the server. There are major issues of security and usability there, though--obviously, your shell is exposed over the web browser which scares me silly, and you're only able to operate as the web server's user, which won't get you very far anyway.
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