The question is asked constantly and has no numeric answer, because the number on its own carries no information. Eight AP courses at a school that offers twenty reads differently from three at a school that offers three.
What is actually assessed
Selective universities evaluate the course load in context. The phrase they use is rigour in the context of what was available. A student who took every advanced course the school offered is read as having taken the hardest available path, whatever the total came to.
This is why copying another student's number is unhelpful. The comparison is against the student's own school, not against an applicant elsewhere.
Where the ceiling really sits
The practical limit is not ambition but the calendar. AP exams are held in the same May window, so five exams means five heavy papers inside two weeks, on top of school assessments.
The common failure is not a low score. It is a student who spread thin across six subjects and produced average results in all of them, where three strong scores would have read better.
Choosing depth over breadth
A cluster of subjects pointing at one field carries more meaning than a scattered set. Calculus BC with Physics C and Computer Science A tells an engineering story. The same three replaced by unrelated subjects tells no story at all.
The file is read as a whole. Coherence is the signal, and coherence comes from selection rather than accumulation.
When the school offers nothing
AP courses can be sat as an external candidate, without the school teaching them. For students in Turkey this is the usual route, and it does not weaken the score: the exam and the certificate are identical.
What changes is preparation, which then has to be arranged outside school hours, and registration, which has to be made through a centre that accepts external candidates.
A workable rule
Two to four exams in total, chosen to match the intended field, is enough for most applications. Beyond that the return falls quickly while the risk to grades rises.
The exception is a student applying to the most selective institutions in a subject where a deep record is expected. There the number rises, but it rises inside one field rather than across many.