Heat the oil in a large stockpot over medium heat for 1 minute. Add the onions and garlic and cook until they're soft and transparent, about 5 minutes, stirring occasionally. Add the tomatoes, bay leaves, and thyme and continue to cook 5 more minutes. Add the chicken and the beef ribs and cook until the tomatoes have disintegrated, about 15 minutes, stirring occasionally and skimming the foam from the top of the broth when necessary. Add the green plantains, cilantro, and chicken stock and bring to a boil. Reduce the heat to medium-low and simmer, covered, until the plantains are tender, 30 minutes.
Using a slotted spoon, remove the chicken from the pot and set it aside. Add the potatoes, pumpkin, ripe plantains, yucca and corn and simmer, uncovered, until both are tender, about 20 minutes. Remove the cilantro and the bay leaves and return the chicken to the pot to re-heat it. To serve, arrange a piece of chicken, some beef, plantains, and a few pieces of yucca and potatoes on each plate. Serve the broth in a small bowl, and the aji sauce on the side, along with a bowl of rice, corn, some avocados and arepas or tortillas on separate plates.