Is there a general rule of thumb like there is for SAT/ACTs (1500+/34+)?
Yes, 1550+ and 35+ would be ideal, but 1500+/34+ isn’t too bad either.
There are exceptions to this, but if you’re a top academic, you should aim for these scores atleast to maximise your chances of even getting considered properly.
Sorry I meant for CIE?
Obviously there’ll be a bit of give or take either way, but I’d be looking to get solid A* grades in all my subjects - this will give you a good academic base, and any top in country or top in the world awards will also come in handy. However in saying this, don’t shy away from taking extra subjects for fear of ruining a perfect academic record - even if you only get, say, an A in a self-studied subject, it’ll still add a lot of value to your application.
The American process is very holistic so CIE grades alone will never “qualify” your application.
From the CIE students I know who have gotten into HYPS, they have A* for most of their subjects (maybe an A in a weak subject).
Most would take at least 5 A-Levels, and recently there’s been a high number of students with 6, 7, 8 A-Levels.
Due to the high number of high-achievers studying CIE, you not only want to aim for A*, but for solid A* (93%+) to stand out further.