This paper describes a memory organization that supports intelligent memory-based argumentation. Our goal is to build a system that can argue opposite sides of an issue by retrieving stories that support or oppose it. Rather than attempting to determine how a story relates to a point on the fly, we explicitly represent the points that the stories support or oppose, as well cis how they support or oppose those points. We have developed a hierarchy of story point types; associated with each type is a set of rhetorical templates, which describe the ways that a story could support or oppose a point of that type. Each template consists of a series of assertion types on which the argument depends. This enables the program to attack intelligently the foundations of the point it is trying to refute. Our approach is being developed within the context of the ILS Story Archive, a large multimedia case base which includes stories from a wide variety of domains.