With the development of hardware accelerators and their corresponding tools, evaluations have become more affordable through fast and massively parallel evaluations in some applications. This advancement has drastically sped up the runtime of evolution-inspired algorithms such as Quality-Diversity optimization, creating tremendous potential for algorithmic innovation through scale. In this work, we propose MAP-Elites-Multi-ES (MEMES), a novel QD algorithm based on Evolution Strategies (ES) designed for fast parallel evaluations. ME-Multi-ES builds on top of the existing MAP-Elites-ES algorithm, scaling it by maintaining multiple independent ES threads with massive parallelization. We also introduce a new dynamic reset procedure for the lifespan of the independent ES to autonomously maximize the improvement of the QD population. We show experimentally that MEMES outperforms existing gradient-based and objective-agnostic QD algorithms when compared in terms of generations. We perform this comparison on both black-box optimization and QD-Reinforcement Learning tasks, demonstrating the benefit of our approach across different problems and domains. Finally, we also find that our approach intrinsically enables optimization of fitness locally around a niche, a phenomenon not observed in other QD algorithms.