Okay, I took two square tomato cages and stacked them. Tied them with garbage bag ties. Then, every two to four inches (don't remember what the spacing's supposed to be off hand), I wove fishing line up, up, up to the top, for the plants to climb. In all it's about nine feet tall, and my beans love it (actually I have three now). It takes a good hour or so to do, but in the end is so worth it! It's rather intensive, though, so be sure to rotate where you put the towers year to year. Mine all do great. On one I put green beans, on one I put wax beans, and on one I put soup beans.
Sooooo, I guess if you have the round cages, perhaps you should stack another cage upside down on top of the first one, and see how that works for you, unless you want to invest (they're not that much, really) in new cages?
Have fun. I love beans!
