In this work, a novel distributed search-planning framework is proposed, where a dynamically varying team of autonomous agents cooperate in order to search multiple objects of interest in 3D. It is assumed that the agents can enter and exit the mission space at any point in time, and as a result the number of agents that actively participate in the mission varies over time. The proposed distributed search-planning framework takes into account the agent dynamical and sensing model, and the dynamically varying number of agents, and utilizes model predictive control (MPC) to generate cooperative search trajectories over a finite rolling planning horizon. This enables the agents to adapt their decisions on-line while considering the plans of their peers, maximizing their search planning performance, and reducing the duplication of work.