The exploration of a system of systems (SoS) tradespace is made much more efficient and effective with a method to first automatically screen a large number of SoS designs for feasibility. This is because not every combination of constituent systems is capable of forming a viable SoS, much less form a SoS that exhibits the desired emergent behavior(s). The SoS Architecture Feasibility Assessment Model (SoS-AFAM) assesses the feasibility of the physical communications, process, and organizational architectures of a SoS. The model applies algorithms based on the minimum requirements for viability relevant to all SoS such as connectivity and completeness. We present a case study to demonstrate how the algorithm can greatly prune the SoS tradespace of infeasible SoS design points, which can increase the efficiency of design exploration.