I was specifically told by one of the secretaries of the board that if you have 6, include them all. The way they explained it, whether you submit 3 or 6, they will probably not read too much into them, but they will at least glance at each one.
For what it's worth, this is my take and what I did/why I included 6.
Call me confident or arrogant but I knew I had good chances. How to show them I'm worthy? By highlighting how I embody the whole-person-concept in these letters.
One LoR was about how I am committed to physical fitness beyond what the APFT requires.
Another focused on my high GPAs which demonstrates scholastic aptitude.
Another one focused on my leadership abilities. Even in the one from a run off the mill retail job, my former boss made sure to emphasize my work integrity and trustworthiness.
See where I'm getting at? Not everybody knows/respects you for the same reasons but all these different reasons show what kind of person you are.