In the previous post's comments, Eva asked where Claire was while Katherine was sobbing and wailing. I completely forgot to talk about the twin aspect of this, and I really should have, because it was a big mental stumbling block for me. In practice, it worked itself out pretty well.
The girls sleep in the same room, and this has been a problem at times. Katherine is the heavier sleeper, and will often snooze right through her sister's crying, but Claire usually wakes up when Katherine does. This may also have something to do with Katherine's vocal abilities -- I think she'll make a fine opera singer someday, because the child is LOUD. So when I was pondering CIO, I knew that the second baby was going to complicate matters a good bit.
I should expand a little bit on the first night of the New Sleep Regime. When G got home from work at 7 PM, the babies had been up since 5 AM with no naps at all, and were both screaming from sheer exhaustion. I was feeling awfully ragged myself, and I said, let's put them in the car and drive around while we talk about crying it out. I knew the girls would probably wake up when we brought them in the house (they are still in the infant seats, though not for much longer), but that way, I figured at least they'd have gotten a car nap while we decided what to do. We drove around for a while, and while Katherine woke back up when we got home, Claire actually stayed asleep. She spent the whole of Katherine's bedtime struggle downstairs in her carseat, and once Katherine was asleep, we were able to transfer her to her bed without waking her.
On subsequent baby-downings, we simply got Katherine settled down first before putting Claire down, and that has worked pretty well. We did have a backup plan in place, though, which was to put one girl in the nursery and the other in the pack-n-play in our bedroom. I think that if both of your babies are lighter sleepers, it might be wise to plan on separating them for the first few days of the sleep experiment.
One of the sleep books I skimmed, I don't remember which one, actually specifically addressed the question of multiples, too. It suggested simply doing it one baby at a time, sorting out the sleep problems of one twin before moving onto the next. This seems pretty self-evident, and I've heard it mentioned in the context of potty training, but I'm not sure that I would have come up with it on my own in re sleep.
One other thing I thought of re multiples and sleep is that, as a mother of twins, I'm already somewhat more accustomed to hearing my babies cry than a singleton mother would be. You can't always sort out the needs of two babies at one time, and while they haven't exactly learned to be patient (as well-meaning people say they will), I have at least absorbed the lesson that they won't die from it. It's not like we're talking about bawling alone for hours, and I don't think that crying in the crib with Mama right there for reassurance is fundamentally different from crying on the floor while Mama's taking care of sister.
What's surprised me most about this whole thing is how quickly the girls have adapted to it. In less than a week, we've pretty much managed to sort out all of our sleep issues, and you can all start hating me again (as I write this, they have been napping for over two hours). I would absolutely not have done this for more than a short time if I hadn't seen that it was working. I figured a couple nights of crying wouldn't scar them for life, but I was not prepared to do so night after night after night. If you're thinking about trying it, I think you'll know relatively quickly whether it will work for you; if it does seem to work for one baby, it's worth making some temporary accommodations for the other one.