Advising interactive commands

[Ag Ibragimov]

Can someone please clarify my confusion about advising interactive commands? 
For some reason, I am unable to advise commands with interactive parameters. 
So, check this out:

(defun my-command (file)
  (interactive (list (read-file-name "Find file: "))))

When called, it prompts to select a file, alright?

Now, if I do this:

(defun my-command-override ()
  (message "running override"))

(advice-add 'my-command :override 'my-command-override)

I expect my new function to run instead, right? And indeed, this works:

(funcall 'my-command) ;; immediately shows the message

However, for whatever reason the following doesn't:

(call-interactively 'my-command)

Meaning, that it doesn't fully override it when called from M-x menu. I mean, 
it would prompt for the file but only after that it would call 
my-command-override. Why is that? Is this expected? If it is, how do you advise 
such commands so they don't show prompts for their parameters?