I have no idea. When I click on it it opens up a “new reply” box with just the one quote that I clicked on, and I don’t know how to make it, well, multi-quote.
I’m betting you’re running Firefox with NoScript, or some other script prevention software. (I just forbade the site and got the same behavior you’re describing.) Allow straightdope.com, and when you click on the multiquote button, it won’t take you to a new window but will instead turn red. Unless you click it again to turn it off, the next time you click Reply or Quote, any post you’ve clicked on will appear in the reply box.
I’m reading the question as more basic – the answer is to click on the square box with "/+ to the right of the “quote” button at the lower right of each post that you want to quote, in the order you want to quote them in, then hit “new reply” (not quick reply). They should all be thre then.
I see that kind of questions often in forums, maybe the Dope could come up with a sticky with the basics about most tasks dopers will have to do when posting.
Ok, no it doesn’t work like that, and it doesn’t turn red, either. It just acts like a quick quote button - I don’t get a chance to click on multiple posts. As soon as I click on one it goes to the reply box and shows that quote.
I will check it at home - if it works there, then my company has probably blocked the Java or whatever that allows it.
You could also hit the multi-quote button on the earlier post(s) you want, and then hit the “Quote” button on the very last one you want to quote. All of them will show up in your post. It’s one less button-click that way.
This is the result of following twickster’s steps. Her “new reply” is actually “post reply” on my screen. (Or at least that’s what I used).
Ok, yeah, my quote button and multi-quote button function exactly the same. Hmm, shall try at home.
Oops, yes, that is correct. Should I go back and fix my box, or would that just confuse things further?
Hm, then I don’t know – try what Bosstone suggested.
If you fix yours, then you can delete my reference to it, and then only the people who have posted (or read) already will be confused. 
The gist of your explanation is the important part IMHO.
’Mika, it works like that for me, too - just like the regular quote button. However, if I then go to a different thread and go to Advance Post, lo and behold, everything shows up there. I copy it all, go back to whatever thread I was in originally, paste, and go on with my comments.
Tedious, to be sure. If I got it to work properly I’d probably go all ShotFromGuns on everybody, so it’s probably just as well.
I’d prefer the method I usually wind up using. Just quote one person, respond to them, copy it, then quote the next person and paste.
(The reason I do it that way is that I immediately quote someone when I think of something to say, and write it down so I don’t forget. Then when I’m finished with the thread I revise it.)
Eureka! I had never noticed this until now. Until this, multi-quoting was a Herculean task of digital labor. Woot!
Ok, it works fine at home, so it’s something to do with the office settings. I’ll just leave it as is. It’s a pity, because it’s a great feature.
Hmm…Maybe I could slip something to my friend in the IT department.
A crisp, unused note? A pill of dubious origins?
Both these buttons have the same base hyperlink, so if they’re functioning the same for you it is certainly because the javascript function that is supposed to trigger when you click multi-quote is being blocked in some way.
Chocolate, I was thinking.
I agree. Thank you for starting this thread, Anaamika.
The classic bribe for IT people used to be Cheetos and Mountain Dew. Sometimes beer and pizza, depending on the age. All of the above will work on my brother, along with roast chicken.