>The goal is to limit those as much as possible, but they'll still happen. "Fixed price" is largely not fixed anyways, as you should always account for change requests and other budget altering mechanisms. I don't think I've ever seen a non-trivial project not have some level of change once work has started.

These need to be handled as separate change orders. Following the model, price the scope changes appropriately based on clearly defined requirements. This part takes some finesse. Many clients may not realize how they can achieve their goals in the most cost-effective manner.