imo yes, you can serve more than one patient with the same caregiver card, provided you have a signed agreement. For example, I recently took on a new patient. After sending in $ to the state, getting the caregiver card, AND providing some free initial meds to this person, they sorta disappeared. Now I have a card for which I could sign on another patient.
You can provide meds to people you don't have a agreemet with, but cannot get anything of value for it.