The simultaneous segmentation of multiple objects is an important problem in many imaging and computer vision applications. Various extensions of level set segmentation techniques to multiple objects have been proposed; however, no one method maintains object relationships, preserves topology, is computationally efficient, and provides an object-dependent internal and external force capability. In this paper, a framework for segmenting multiple objects that permits different forces to be applied to different boundaries while maintaining object topology and relationships is presented. Because of this framework, the segmentation of multiple objects each with multiple compartments is supported, and no overlaps or vacuums are generated. The computational complexity of this approach is independent of the number of objects to segment, thereby permitting the simultaneous segmentation of a large number of components. The properties of this approach and comparisons to existing methods are shown using a variety of images, both synthetic and real.