What alterations can result in the permit for use (Betriebserlaubnis) being cancelled?

You answered correctly. The permit for use (Betriebserlaubnis) of a vehicle can be cancelled if you make alterations that are not allowed or not approved. Fitting a sidecar or using tyres of a different size can significantly change how the vehicle handles or its safety, so these modifications require approval and, if not done properly, can lead to losing the Betriebserlaubnis. Simply fitting a rear fog lamp does not cancel the permit, as this does not fundamentally alter the vehicle’s characteristics. Always ensure that any modifications to your vehicle are registered and approved if required to avoid losing your permit.