Medical school applicants sometimes worry about adversely affecting their chances of admission because they might "offend" one school by applying to others. Good news: Schools will not know which other institutions or how many other institutions you applied to through AMCAS.
However, later in the season, medical schools at which you are accepted will be able to see at which other schools you are holding acceptances. But, of course, at that point, it's too late for that information to harm you.
So, rest assured, applying broadly will not adversely affect your chances at an individual school.