Rather than obtaining a single good solution for a given optimization problem, users often seek alternative design choices, because the best-found solution may perform poorly with respect to additional objectives or constraints that are difficult to capture into the modeling process. Aiming for batches of diverse solutions of high quality is often desirable, as it provides flexibility to accommodate post-hoc user preferences. At the same time, it is crucial that the quality of the best solution found is not compromised. One particular problem setting balancing high quality and diversity is fixing the required minimum distance between solutions while simultaneously obtaining the best possible fitness. Recent work by Santoni et al. [arXiv 2024] revealed that this setting is not well addressed by state-of-the-art algorithms, performing in par or worse than pure random sampling. Driven by this important limitation, we propose a new approach, where parallel runs of the covariance matrix adaptation evolution strategy (CMA-ES) inherit tabu regions in a cascading fashion. We empirically demonstrate that our CMA-ES-Diversity Search (CMA-ES-DS) algorithm generates trajectories that allow to extract high-quality solution batches that respect a given minimum distance requirement, clearly outperforming those obtained from off-the-shelf random sampling, multi-modal optimization algorithms, and standard CMA-ES.