Enabling vertical-stack proximal cooperation between multirotor flying robots can facilitate the execution of complex aerial manipulation tasks. However, vertical-stack proximal flight is commonly regarded as a dangerous condition that should be avoided because of persistent and intense downwash interference generated between flying robots^1,2. Here we propose a cooperative aerial manipulation system, called FlyingToolbox, that can work stably with sub-centimetre-level docking accuracy under vertical-stack flight conditions. The system consists of a toolbox micro-aerial vehicle (MAV) and a manipulator MAV. The robotic arm of the manipulator MAV can autonomously dock with a tool carried by the toolbox MAV, in which the docking accuracy reaches 0.80 ± 0.33 cm in the presence of downwash airflow of up to 13.18 m s⁻¹. By enabling midair tool exchange in proximity, FlyingToolbox resolves the paradox between flight proximity and manipulation accuracy, suggesting a new model for heterogeneous and interactive flying robot cooperation in diverse applications^{3, 4–5}.