While humans routinely encode and retrieve memories in groups, the bulk of our knowledge of human memory comes from paradigms with individuals in isolation. The primary phenomenon of interest within the relatively new field of collaborative memory is collaborative inhibition: the tendency for collaborative groups to underperform in free recall tasks compared to nominal groups of the same size. This effect has been found in a variety of materials and group compositions (Rajaram & Pereira-Pasarin, 2010). However, the majority of research in this field is guided by verbal theories without formal computational models. In this paper we adapt the Search of Associative Memory (SAM; Raaijmakers & Shiffrin, 1981) model to collaborative free recall. We present a framework to scale SAM to collaborative paradigms with multiple SAM models working together. Our simulation results with the collaborative SAM model suggest that retrieval disruption, responsible for the part-set cuing effect in individuals, is also the cause of collaborative inhibition when multiple models are working together. Our work provides an existence proof that SAM can act as a unified theory to explain both individual and collaborative memory effects, and offers a framework for future predictions of scaling to increased group sizes, shared knowledge, and spread of false memories.