Александр

class Entity {
}

class EntityException extends \Exception {
    private $entity;

    public function getEntity() {
        return $this->entity;
    }

    public static function create($entity, $message = 'Error', $code = 0)
    {
        $exception = new static($message, $code);
        $exception->entity = $entity;
        return $exception;
    }
}


try {
    throw EntityException::create( new Entity, 'Internal error' );
} catch(\EntityException $e) {
    // Handle entity exceptions
    echo $e->getMessage() . PHP_EOL;
    var_dump($e->getEntity());
} catch(\Throwable $e) {
    // Handle other exceptions
}