We present a technique designed for parallelizing large rigid body simulations, capable of exploiting multiple CPU cores within a computer and across a network. Our approach can be applied to simulate both unilateral and bilateral constraints, requiring straightforward modifications to the underlying physics engine. Starting from an approximate partitioning, we identify interface bodies and add them to overlapping sets such that they are simulated by multiple workers. At each timestep, we blend the states of overlap bodies using weights based on graph geodesic distances within the constraint graph. The use of overlap simulation also allows us to perform load balancing using efficient local evaluations of the constraint graph. We demonstrate our technique's scalability and load-balancing capabilities using several large-scale scenes.