In this paper we show how taking advantage of autonomous agents' capability to maintain parallel interactions with others, and incorporating it into the cooperative economic search model results in a new search strategy which outperforms current strategies in use. As a framework for our analysis we use the electronic marketplace, where buyer agents have the incentive to search cooperatively. The new search technique is quite intuitive, however its analysis and the process of extracting the optimal search strategy are associated with several significant complexities. These difficulties are derived mainly from the unbounded search space and simultaneous dual affects of decisions taken along the search. We provide a comprehensive analysis of the model, highlighting, demonstrating and proving important characteristics of the optimal search strategy. Consequently, we manage to come up with an efficient modular algorithm for extracting the optimal cooperative search strategy for any given environment. A computational based comparative illustration of the system performance using the new search technique versus the traditional methods is given, emphasizing the main differences in the optimal strategy's structure and the advantage of using the proposed model.