Multi-agent human-robot co-manipulation is a poorly understood process with many inputs that potentially affect agent behavior. This paper explores one such input known as interaction force. Interaction force is potentially a primary component in communication that occurs during co-manipulation. There are, however, many different perspectives and definitions of interaction force in the literature. Therefore, a decomposition of interaction force is proposed that provides a consistent way of ascertaining the state of an agent relative to the group for multi-agent co-manipulation. This proposed method extends a current definition from one to four degrees of freedom, does not rely on a predefined object path, and is independent of the number of agents acting on the system and their locations and input wrenches (forces and torques). In addition, all of the necessary measures can be obtained by a self-contained robotic system, allowing for a more flexible and adaptive approach for future co-manipulation robot controllers.