I'm not sure if the continuity of care is a done in Reggio or not. Our focus, in addition to being inspired by the Reggio approach, is Attachment Theory. That is the basis of our work. To faciliate the attachment of the children with their primary caregiver and each other, we all stay together. It is wonderful, because we get to know each other and build from that relationship as we grow, rather than having to start over each year. This is only my second year, but I've seen how nice it is to know some of my children since they were 18 months old, and now they are almost 3. My daughter started at the school when I did and she was 2. She bonded with a little girl in her group last year and now they are inseparable. Both of them are only children, and they act like sisters. They also really love their teacher and it is very sweet to see how close they all are. They know each others needs and wants, and will know just what another child will want to comfort them (like bringing a favorite toy when a child is hurt).
I know that it is very difficult to do here in the US though. For one thing, there is such high turn-over of teachers here due to the low pay, teacher burn-out, low status (people view Preschool teachers as not REAL teachers) etc. Our school came up with a concept of a Staff Stability Fund, which works in our community mostly because the school serves affluent families. They are mostly families where both parents work full-time, so the children are in full-time care. They pay an extra $1,000 /year that goes into a fund. When the children graduate to kindergarten, their teacher receives the Staff Stability money. But if the teacher leaves before the end of that time, then they don't receive the bonus. It is an extra incentive to keep them at the school, and thus retain the attachment.
I know that some schools try to provide at least primary caregiving, but it is difficult to do. When people look for schools, I recommend finding schools that provide primary caregiving and/or continuity of care even more importantly than being a Reggio inspired school. But that is just my opinion.