Hanoverian/TB Cross - Registration

Curious as to what registries a foal out of a Hanoverian mare registered in the main mare book by a Thoroughbred stallion would be eligible? I understand that the foal will be given a COP but any COP foal and its offspring would not be inspection-eligible. Are there other registries in which the foal, if a filly, could be registered and inspected into a breeding program?