Author Bill Harley calls this a "zipper" song. He defines a zipper song as one where each verse is the same except for one word being changed. He gives as an example Pete Seeger's If I Had a Hammer. In Sitting Down to Eat, the singer relates the story of being all set to eat when an animal appears and askes to join him. "If you've got enough for one, then you've got enough for two," the animal reasons, and that always makes sense to the singer. This continues until there are nine animals (well, 8 animals and the singer) sitting down to eat, including a crocodile and even a whale. But when the tiny caterpillar asks to join them, it's just too much.
This would be a good story to tell with the audience joining in -- they'll be able to remember the refrain easily.