Controlled manipulation of multiple objects whose dynamics are closely linked is a challenging problem within contact-rich manipulation, requiring an understanding of how the movement of one will impact the others. Using the Jenga game as a testbed to explore this problem, we graph-based modeling to tackle two different aspects of the task: 1) block selection and 2) block extraction. For block selection, we construct graphs of the Jenga tower and attempt to classify, based on the tower's structure, whether removing a given block will cause the tower to collapse. For block extraction, we train a dynamics model that predicts how all the blocks in the tower will move at each timestep in an extraction trajectory, which we then use in a sampling-based model predictive control loop to safely pull blocks out of the tower with a general-purpose parallel-jaw gripper. We train and evaluate our methods in simulation, demonstrating promising results towards block selection and block extraction on a challenging set of full-sized Jenga towers, even at advanced stages of the game.