If the plants are already wrapped around the tomato cage then leave it be and don't try to take it out. Yes, you can put a taller trellis beside the tomato cage to have the plants grow on it. Try to use something at least 6 feet tall.

Rodney

You can stack tomato cages on top of each other.

You could also stick a few wooden poles inside the cage (pushing them down into the soil some) and let the beans continue to climb up them. Cattle panels make excellent and long-lasting trellises and might be something for you to consider in the future.

...or 2” x 3” vinyl coated mesh fencing attached to two of poles. It rolls up for easy storage and lasts for years.

tj