Is it acceptable to add a result to a paper when a journal asks for revisions?

You can make whatever changes you like in revision. The key point is that the paper is being refereed again. (Maybe the referee isn't paying so much global attention to your paper the second time around. But by the way, maybe the referee wasn't paying so much attention the first time around! There are never any guarantees of that, but you have done your due diligence.)

It is quite common for revised papers to contain many small to moderate changes, including those that were not called for by the referee. If you think about it, it is probably better not just to make precisely the changes asked for -- you are also responsible for your paper as a holistic document, and localized technical changes may necessitate other changes for the sake of unity, coherence and so forth. However, as a referee it is a bit disconcerting to get a paper that has too many changes I have not asked for: at a certain point it begins to feel that I have to referee two papers when I have agreed to referee one. For instance I recall getting a revised paper that was almost 10 pages longer, and I didn't like that much (but I did recommend it for acceptance).

As an author I can think of several cases where I have added significant material to the paper in revision, so it certainly does happen, and at the moment I cannot recall a situation where adding the material seemed to adversely affect the status of the paper. If there is one extra result that you want to put in the paper and its proof takes only a couple of pages, I think you should probably go ahead.

Although I think you'll get away with it fine, whether it is really better to put more theorems into a math paper in revision is a different question that I am a bit too daunted to fully address here. It depends on so many other factors, many of which are cultural. E.g. another answer writes:

I would lean towards publishing a followup paper instead. Does more for you on pub count.

In most parts of pure mathematics having "more papers than theorems" or "more papers than ideas" is looked down upon. If in a certain paper you prove four cognate theorems and then later you try to write up a paper on a fifth cognate theorem, there is a good chance that the journal in which you can publish that little paper is so much worse than the first journal that it doesn't specifically help your career to do so. Whereas if you just appended the fifth theorem in the first paper, you probably wouldn't get any more credit for that either...but at least the fifth theorem would appear in print with little additional trouble on your behalf. I can definitely think of theorems that I have added to papers in this way (not necessarily literally in revision; sometimes just as offshoots of the main project): I proved them so I want to publish them, but I do not always want to play the "How good is this?" game if I don't have to.

This is the sort of question to ask the editor. If it is a small change it might be fine. Anything bigger could, perhaps, require another round of review to assure the editor.

Another paper would be a good thing, of course, if you can publish it, perhaps augmenting it with more results to make a more complete whole. But, you need to write it up in any case unless you intend to just abandon it. If it is in the current paper, its significance might not be noticed, of course. But if it is relatively insignificant it might not actually matter to the editor.

You could ask the editor now, which might save some effort. But you could, perhaps, also add it to the next (final?) version if acceptance comes soon. But warn the editor about what you have done so that it is clear. Editors probably don't like surprises.

This is actually quite common, that by the time the referee report comes you may have a bit more to say. Or the extra bit may come from the revision process itself. It is fine to add it to the paper. Indicate the addition when you send the revised version.

(Quite common: this has happened to many papers I've refereed and to some of mine as well. And I have anecdotal evidence from several colleagues that this is indeed usual.)

Of course, if rather than a bit more you have significant material to add the situation is different: the decision seems now to be whether to write a sequel, to discard the current one, or to thoroughly revise it.