I am planning to pursue my PhD in business administration. I would like to apply to more than one school to get an admission because business schools are competitive. Can I submit my research interest (proposal paper) in the application to more than one school if the faculty in each school have the same research area or is my application going to be rejected because I submited it to more than one school and that is considered to be plagiarism?
Why would this constitute plagiarism?
First, you wrote it, so it could at best be self-plagiarism.
Second, a proposal paper or expression of research interest is expected to be send to more than one institution. Sending them is not tantamount to a publication. You do not even have to mention this, since every-one on an admission committee will assume that you are applying to more than one institution.
If you do not get accepted, you would be free to resubmit the expression of research interest to the same institution the next year.