The typical recommendation would be the
Yakima Load Warrior luggage basket. The Yakima LoadWarrior gear basket would mount to the Yakima Q Tower roof rack on your 2004 Hyundai Sonata and the Yakima Sidewinder tandem carrier would then attach directly to the two integrated cross bars on the Yakima Load Warrior gear basket.
Unfortunately, your 2004 Hyundai Sonata roof rack setup is not rated to safely handle this much weight and is deemed unsafe by the car rack manufacturers. Your Huyndai Sonata rooftop is not strong enough for all this weight. You can, however, still mount the
Yakima BasketCase cargo roof basket to the Yakima Q Tower crossbars alongside the tandem bike carrier and you will have a very safe solution for carrying your luggage gear and tandem bike simultaneously on the 2004 Hyundai Sonata roofrack. The Yakima BasketCase does not offer quite as much cargo capacity as the Yakima LoadWarrior luggage basket does but you will still be able to haul a lot of cargo ontop. A good tip for making the Yakima Basket Case fit next to the tandem bike rack is to turn the BasketCase so that it extends lengthwise from front to back of your rooftop, this position will allow plenty of room on your crossbars for both the luggage basket and the tandem bike carrier at the same time.