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A caller can move an appointment they already have. The agent re-checks availability for the new time and reads the exact new date and arrival window back before confirming.
How rescheduling works
The agent finds the caller's appointment by their phone number. If they have more than one, it reads the options and asks which to move — it never guesses. It then checks the new time against real availability and confirms only if it fits.
The new time is interpreted in the appointment's location timezone, so a business spanning timezones does not shift a job by hours.
When the new time does not fit
If the requested time is not available, the agent offers the nearest times that are. Nothing is moved until the caller agrees to a time that fits, and the agent reads the exact new date and time back before finishing.