Create breadcrumbs based upon taxonomy

Summary: How to do the below? Even some general guidance would be great!

We have a complicated taxonomy with lots of parent terms with children terms underneath. Our pages are generated by a behind the scenes call to that taxonomy term. So for instance, if you're looking at the Teen section, all the posts shown have the tag "Teen" on them. A post can be set to multiple taxonomy terms at the current time.

We'd like to develop breadcrumbs so that if you're looking at an item which is tagged Teen as the parent term and Movies as the child term, the breadcrumb would show something like Home > Teen > Movies > Movie Title

Do you know if there is way to do this despite there being multiple taxonomy terms? I'm thinking of enforcing a "choose one taxonomy term and stick to it" approach otherwise so we can have our breadcrumbs!