Improved collaboration techniques for tasks executed collectively by multiple agents can lead to increased amount of information available to the agents, increased efficiency of resource utilization, reduced interference among the agents, and faster task completion. An example of a multiagent task that benefits from collaboration is Collective Transport with Obstacle Avoidance: the task of multiple agents jointly moving an object while navigating around obstacles. We propose a new approach to sharing and aggregation of information among the transporting agents that entails (1) considering all available information instead of only their own most pressing concerns through establishing objectively valued system needs and (2) being persuadable instead of stubborn, through assessing how these needs compare to the needs established by their peers. Our system extends and improves upon the work in (Ferrante et al. 2013), leading to better informed agents making efficient decisions that cause less inter-agent interference and lead to faster and more reliable completion of the collective task.