There is no magic number, and interviewers are generally not counting ideas like points on a test. The quality, breadth, and organization of the answer matter more than hitting five or six items.
Three strong ideas can be enough if they cover meaningfully different angles and you explain why they matter. Three versions of the same idea, however, will feel narrow even if each one is technically reasonable.
A useful habit is to give your best ideas first, then pause and check whether you have covered the major categories. If there is an obvious gap, add another idea. If the answer already feels complete, forcing weak extras can actually make it worse.
Think breadth plus depth, not raw quantity. You want the interviewer to see that you can generate options and prioritize them, not that you can produce the longest list. A useful reference is the case interview problem-solving cycle if you want to go deeper on that part.