Sharing multimedia content, without obtaining consent from the people involved causes multiparty privacy conflicts (MPCs). However, social-media platforms do not proactively protect users from the occurrence of MPCs. Hence, users resort to out-of-band, informal communication channels, attempting to mitigate such conflicts. So far, previous works have focused on hard interventions that do not adequately consider the contextual factors (e.g., social norms, cognitive priming) or are employed too late (i.e., the content has already been seen). In this work, we investigate the potential of conversational agents as a medium for negotiating and mitigating MPCs. We designed MediationBot, a mediator chatbot that encourages consent collection, enables users to explain their points of view, and proposes solutions to finding a middle ground. We evaluated our design using a Wizard-of-Oz experiment with 𝑁 = 32 participants, where we found that MediationBot can effectively help participants to reach an agreement and to prevent MPCs. It produced a structured conversation where participants had well-clarified speaking turns. Overall, our participants found MediationBot to be supportive as it proposes useful middle-ground solutions. Our work informs the future design of mediator agents to support social-media users against MPCs.