Yes, a MOC can nominate a candidate to multiple SAs. Most MOCs will ask you to rank your SA preference on their application in an effort to nominate you to your first choice. However, last year DS received a nomination from Congressman Yarmuth for both USAFA and USMA. He then decided to focus on USAFA, so he declined the nomination to USMA so that it could go to someone else. Keep in mind that Kentucky is not super competitive like VA or CA. I believe that Yarmuth did not fill all his nomination slates for every SA. But at the Senatorial level, even Kentucky had over 50 applicants for the 10 nomination slots for each Senator. More competitive states have hundreds of nominees for each Senatorial slate of 10.
It is my understanding that by law a QUALIFIED principal nominee must be offered an appointment. Qualified means they are academically, medically, and physically qualified. But I would be concerned if I was a male candidate that is unable to do a single pull up. I am not sure that meets the minimum physical qualifications.