eTermin offers you the option of setting deadlines for canceling appointments (globally or individually for each service). You can use it to specify up to which point in time before the appointment your customers can cancel the appointments themselves.
The same specified value is being taken into account when a customer wants to change their appointment for another day.
You can define the global cancellation period under Company > Settings > Communication > Appointment cancellation deadlines.
You can also specify for each service when the last possible cancellation time is before the actual date. To do this, click on Company > Services > 'Edit' desired service > Service-specific settings > Appointment cancellation deadline and select the desired deadline.