I often want to address someone in a thread, but then I also want to address the OP. I think some sort of separation is needed, and wonder if making two posts is okay. I’ve tried it both ways, and no one has said anything.
Anyways, while I’d be glad to hear from moderators, I have a feeling the answer is a courtesy based one. So I’m making this a poll, as well.
I voted yes, but my own non-official opinion is that it’s a matter of personal preference.
I voted, as a moderator, that you can make as many posts in a row as it takes. Just as long as they’re good posts, to the point and appropriate to the OP/thread.
I do it myself as a poster, and of course have no problem with it as a moderator.
I think it’s often reasonable if you are addressing two different posters. It can also be warranted if you think of additional points after the edit window has expired.
It can get a bit annoying if a poster makes a half dozen posts in a row, because they haven’t thought their arguments through. But I don’t see a problem with two or three posts in a row.
BigT: Either approach is acceptable (from the point of view of rules and etiquette of the SDMB), assuming it doesn’t get out of hand.
samclem, you say “as many posts in a row as it takes,” but I assume you agree there’s some sort of limit. That is, 27 separate posts to address 27 different comments in 27 earlier posts in some long thread would be… well, over the top.
Frankly, my personal pref is to put them in one post, separating by paragraphing and using quote-tabs or intros. I assume that use of quote-tabs is obvious, and I’ve used “intros” and paragraphing in this very post to make it clear that I’m addressing different points raised by different posters in two different earlier posts.
I think it sort of depends on (a) how many, and (b) how inter-related, and © what’s easiest for the reader to follow.
I voted “another context” because usually multiple posts can be addressed in one response. The exceptions I see are: if you are replying to many comments your one post may end up huge and if the two posts you are replying to are of wildly different tone. Sometimes in the MMP you want to respond to something serious (eg the death of a loved one) and something lighthearted (eg flirtatious banter). One post, putting them together, would seem inappropriate.
Personally, aesthetically, I don’t like multiple posts in a row, each responding to someone different.
I voted for all three choices because I feel that it depends on the situation. You don’t want to take up most of a page with your responses (it’s happened a few times, and it’s annoying as hell), but separating your replies can be useful for providing clarity. I think it all depends on the situation and on personal preference. For me, as a reader, two or three would be fine. More than that gets iffy.
I don’t really feel that strongly about it, but I say just use one post while making it clear who you’re responding to in each section of the post. Another post should only be used if you came across someone else you want to respond to later in the thread (or you need to clarify, forgot to say something, have something to add, etc) after you’ve already posted once and the edit window’s closed.
Some boards (usually ones where you can edit at any point) forbid posting more than once in a row in a thread, but I wouldn’t want to see something that strict happen here. At least one board I’ve been to even has it set up where if you post multiple times, it automatically merges the posts into one (or maybe mods come in and do that manually, I don’t know.)
I didn’t exactly answer the question as asked; I voted “Nope,” but I think it’s perfectly OK to split them up, and that it’s preferable at times. The multi-quote feature makes it easy to properly attribute quotes and address posters accordingly, and that’s what I think is best. But sometimes, I’ll have replies that address completely different issues, and it makes no sense to keep them together, so the toothache-inducing pun will go in one post, and the thread-killing definitive argument in another. Normally, however, any number of not-so-definitive arguments can go in one post, even if one makes an ethical point, while another brings up a historical one, a third criticizes everyone’s spelling, and another accuses people of arguing in bad faith.
I don’t have a problem with multiple posts in a row. As Colibri has said, sometimes you just have to do it. Sometimes I’ll post something in reply to one poster and upon re-reading the thread, I find another poster I want to respond to… and the edit window has closed already… 
So here comes post two. Other times I find that there are multiple conversations going on in one thread, so for the sake of clarity, two posts are almost necessary.
The answer to the question as asked is, “Yes, it is acceptable to post two posts in a row.”
As a personal practice, I tend to try to compose one long post to address all the points I wish to make up to that time in the discussion, and use quote tags and descriptive text to separate the comments. But that does lead for long posts. I can see how shifting tone might feel better as separate posts, but an alternative is something like using a line “___________” to separate the portions and descriptive text. But I don’t worry too much about others who post 2 or 3 comments in a row.
However, if you are posting 3, 4, 5 posts in a row, it begins to look like you aren’t thinking through your posts much, that you are responding to each post as you get to it and not the thread as a whole. That I find mildly annoying. Not something I’d complain about unless it was excessive (27 posts in a row to address 27 different comments?)
The other reason might be needing to respond to multiple points, but not having time to do it all at once. Of course, you would expect somebody else to reply if it takes you any substantial time between posts.