We investigate cooperative fluorescence in a dilute cloud of strongly driven two-level emitters. Starting from the Heisenberg equations of motion, we compute the first-order scattering corrections to the saturation of the excited-state population and to the resonance-fluorescence spectrum, which both require going beyond the state-of-the-art linear-optics approach to describe collective phenomena. A dipole blockade is observed due to long-range dipole-dipole coupling that vanishes at stronger driving fields. Furthermore, we compute the inelastic component of the light scattered by a cloud of many atoms and find that the Mollow triplet is affected by cooperativity. In a lobe around the forward direction, the inelastic Mollow triplet develops a spectral asymmetry, observable under experimental conditions.