It would be great if you studied at the university where you always dreamed about. So some students try to concentrate on application only to their dream universities. But I would not agree with the idea. Because I know that reality is harder than you think. You would not fly, if you did not have wings. You would not fly with the wings, if you did not learn to fly. I would support minimum to three different schools. There are two reasons why it is important.

The first reason is that almost no one can be sure that the student is accepted, even though an applicant is very highly qualified: high scores on SAT and TOEFL. They send more supporting documents to the university and will expect something of course. But students don't know how the selection process at the university exactly works. No applicant would be so sure in the process.

Another reason is that it would be very wise if applicants made universities decide first. If two universities sent you their admissions, you would choose one of them. To select it, there are following relevant points. Beside the name of the universities, you can know who are teaching at the university. If you don't find the right professors for your work at university, it would be the wrong choice. Other important points would be scholarships, grants, accommodations, student jobs, the distance between the university and home, etc.

What I told is just my personal idea, you have to choose on your own. Good luck to all applicants!