Aircraft collision avoidance systems assist in the resolution of collision threats from nearby aircraft by issuing avoidance maneuvers to pilots. Encounters where multiple aircraft pose a threat, though rare, can be difficult to resolve because a maneuver that might resolve a conflict with one aircraft might induce conflicts with others. Recent efforts to develop robust collision avoidance systems for single-threat encounters have involved modeling the problem as a Markov decision process and applying dynamic programming to solve for the optimal avoidance strategy. Because this methodology does not scale well to multiple threats, this paper evaluates a variety of decomposition methods that leverage the optimal avoidance strategy for single-threat encounters.