In this paper we present a novel approach for combining Case-Based Reasoning (CBR)Argumentation. This approach involves 1) the use of CBR for evaluating the arguments submitted by agents in collaborative decision making dialogs, and 2) the use of Argument Schemes and Critical Questions to organize the CBR memory space. The former involves use of past cases to resolve conflicts among newly submitted arguments by assigning them a strength, and possibly submitting additional arguments deemed relevant in similar past deliberations. The latter enables use of agents' submitted arguments instantiating Argument Schemes and Critical Questions, to assess the similarity among cases. This use of CBR and argumentation is formulated with the ProCLAIM model, which features a Mediator Agent that directs proponent agents in their deliberation and subsequently evaluates their submitted arguments so as to conclude whether a proposed decision is valid. To motivate and substantiate the practical value of this approach, we illustrate its application in the human organ transplantation field.