When designing a software architecture to fulfill quality-attribute requirements, architects normally explore and assess alternative solutions leading to different quality-attribute tradeoffs. In this context, we developed the SQuAT framework to support automated multi-objective optimization in large design spaces. SQuAT provides a modular, multi-agent architecture in which each agent represents and optimizes for a particular quality attribute. However, this search strategy has problems identifying tradeoffs that satisfy all the parties (or architects’ concerns), particularly when searching for many candidate solutions and evaluating them becomes computationally costly. This is actually a general challenge for architecture optimization tools. To deal with it, SQuAT features an agent negotiation protocol that seeks consensus based on the utility of solutions as judged by each agent. In this paper, we present a parameterized heuristic that enhances the integration between search and negotiation in SQuAT, and also report on an empirical evaluation with two case studies. The results show initial evidence that using negotiation is more effective than doing a pure search to identify solutions having a balanced utility across agents and, thus, offer alternative quality tradeoffs to the architect.