Within Scheduler Rules & Logic (Settings > Scheduler Rules & Logic) you'll see two customizable features related to appointment rescheduling - a max limit and the ability to restrict any rescheduling to the same staff.
Max Rescheduling Limit: Want to make sure clients don't keep rescheduling over and over and put a cap on the number of times they can reschedule? This feature is for just that. Here, you can put a max rescheduling count in place to limit the number of times they can reschedule.
Restrict Scheduling to Same Staff: If you like the idea of making sure that when clients go to reschedule, they only see options with the initial staff member they booked with, this option is for you. Selecting that option will make it so that if a client goes to reschedule, the same staff member will come up, making it simple for them to reschedule with the initial person.
Remember to save any changes made and they will reflect right away!