Hi Matt - great question!
At this time our Ignite implementation does not support a true reschedule action for a currently booked appointment.
Some developers have attempted to create their own reschedule workflow by canceling and then booking a new appointment, but when doing so that causes problems with any associated encounters and documentation on the old appointment, so we do not support/recommend doing that.
We are not quite yet aligned to have it on our roadmap, but we're keenly aware of the need.
Richard
Product Manger for Scheduling API