It doesn't really improve your chances that much, but since each school has a slightly different way of picking their top applicants you should see which of these schools' policies puts you in the best light.
I was going to have 3 back ups (all were non-profit private schools: Catholic University of America, Stevenson University and Johns Hopkins University). But after realizing that I didn't want to move away from my spouse, or commute I dropped the back-up idea and focused on making myself the best applicant at my number one choice. This made things easier on me as well due to only having to worry about the pre-reqs of one school. It also cut down on application costs (not just $, but time put into essays and getting letters of rec from Professors (are they going to be ok with 10, not likely)).
Narrow your scope, increase your effort and be the best applicant at one school.