CNA in training, how do I ask for a full time position that doesn’t include a set unit assignment.

Let me explain. I’ve been a private caregiver for five years. I decided to become a CNA in order to work in a long-term care facility and work with a variety of patients. I’d rather not work in one section with only a few set patients. I would rather be scheduled to work in all units so that I can become a more well rounded employee and CNA. Is there a place for someone like that in a long term care facility? Or am I asking for something impossible?