Loa and appointment are 2 different things. Loa, are rare, and when they do come out they are a letter of assurance. Meaning, if you receive a nomination and have your application completed and are 100% qualified, you are assured an appointment.
Nominations are academy specific. Meaning, a nomination to air force can only be used for air force. What your senator is saying is, he will only give you a nomination to one academy. However, if you receive an loa to army, and your nomination is to navy, he will change your nomination to navy if you want him to.
Loa, when available and offered are usually done prior to nominations. If you already had a nomination, thered be no need for an loa. They could offer you the appointment. But most MOC require in your application your preference of which academy. Your senator is simply saying, if you apply for one academy, and prior to actually getting the nomination, if you receive an Loa, he will let you change your mind and ask for the nomination to the.academy offering you the Loa.
But bottom line is: you can't use a nomination for more than 1 academy.