I'm going to just dump this as script. If you need it as Quest edit sequences, let me know...

The open command just does this:
TryOpenClose(true, object)
which is quite handy, as it gives you a function to call. So you could do this.
First, add a new "answer" verb. You can easily do that in the editor.
<verb name="answer">
<pattern>answer #object#</pattern>
<property>answer</property>
<defaulttext>You can't answer that.</defaulttext>
</verb>
That creates a default verb which can apply to any object, but by default says, "You can't answer that." Feel free to make that what you want.

Then implement an "answer" attribute on your door object, which will be called when someone types "answer door". Have its script be:
<answer type="script">
TryOpenClose(true, this)
</answer>
You need "this" instead of "object" as the verb is executed in the context of the door object (passed as "this") as opposed to a command which is matching pattern with param "object".)
Hope that helps!
(The other approach which I toyed with but rejected was copying the "open" command up and adding "answer" into the list of choices, but that then meant that any object you could open, you could also answer, which didn't really make sense. I think this is the better approach and in line with Quest's design.)