How many SAT subject tests are recommended in order to apply top 20 schools?

I agree with @Abhishek; two is generally all you need for basically anywhere. Three can be a slight bonus at super super super competitive schools (like HYPSM), but two is still fine for those, and anything over three is basically pointless in the eyes of an admissions committee.

Also, I noticed you mentioned AP scores in your comment. As a sidenote, AP scores do not carry much (if any) weight in admissions. Taking AP classes does matter a lot, but the scores themselves are a lot less significant than the grades you get in the classes themselves. I think that's probably why they didn't make a difference in the chancing system here.

I know you already got your answer but wanted to add I think 2 is good enough too. Of course, check the requirements for each school and see what they suggest. You probably already know this but if a college recommends taking the SAT IIs that is essentially the same thing as requiring them. I think for a lot of schools you will be putting yourself at a disadvantage if you don't.

Thanks, Abhishek, it makes sense. I tried Calculating Chances in this site. And adding more SAT or even more AP test scores didn't boost the chances for most of top schools. Appreciate for your note.