We present PLn, a multi-agent epistemic logic in which each agent can perform uncertain (possibilistic) reasoning. The original feature of this logic is the presence of a distributed belief operator, with the purpose of merging the belief of different agents. Unlike the corresponding operator in the categorical (non-uncertain) case, our distributed belief operator accumulates support for the same fact coming from different agents. This means that opinions shared by different agents can be combined into a stronger distributed belief. This feature is useful in problems like pooling expert opinions and combining information from multiple unreliable sources. We provide a possible worlds semantics and an axiomatic calculus for our logic, and prove soundness, completeness and decidability results. We hint at some possible applications of PLn in the conclusions.