Show the Kappa Alpha Psi recruiting board what makes you a unique candidate. Help them understand what makes you stand apart. Give examples of accomplishments outside academics on your resume or write a personal vitae. Sports, extracurricular activities, volunteer work, awards, steady employment, student government are good examples of how you have spent time productively in the past.
Provide references for the Kappa Alpha Psi recruiting board. You want solid references that are respectable in themselves, not just people who will say nice things about you or fluff your resume. You also want someone who knows you well. The more intimate your relationship with the reference, the more likely he will know something unique about you, something you may not realize is pertinent.
Request a personal interview with the Kappa Alpha Psi recruiting board. Give yourself the opportunity to tell the recruiting board your plans for the future. Tell them what you plan to study, how you plan to spend your free time, and how you plan to maintain a solid GPA while finding time to socialize.
Share something personal from your background. Make yourself more than the application they are reading. Activities, honors and employment are not you; they are simply what you do. Help the recruiting board understand a little more deeply about who you are. In person is best, but if you must, include on your resume or vitae your examples of success. Even small honors count. Help the Kappa Alpha Psi realize that you are an asset.
Request a face-to-face meeting with the Kappa Alpha Psi recruiting board, even if they rejected you the first time. If you can get your foot in the door and speak to them personally you have a much better opportunity of persuading them you are right for Kappa Alpha Psi than if you simply stand on your resume alone.