A recent comparison of well-established multiobjective evolutionary algorithms (MOEAs) has helped better identify the current state-of-the-art by considering (i) parameter tuning through automatic configuration, (ii) a wide range of different setups, and (iii) various performance metrics. Here, we automatically devise MOEAs with verified state-of-the-art performance for multi- and many-objective continuous optimization. Our work is based on two main considerations. The first is that high-performing algorithms can be obtained from a configurable algorithmic framework in an automated way. The second is that multiple performance metrics may be required to guide this automatic design process. In the first part of this work, we extend our previously proposed algorithmic framework, increasing the number of MOEAs, underlying evolutionary algorithms, and search paradigms that it comprises. These components can be combined following a general MOEA template, and an automatic configuration method is used to instantiate high-performing MOEA designs that optimize a given performance metric and present state-of-the-art performance. In the second part, we propose a multiobjective formulation for the automatic MOEA design, which proves critical for the context of many-objective optimization due to the disagreement of established performance metrics. Our proposed formulation leads to an automatically designed MOEA that presents state-of-the-art performance according to a set of metrics, rather than a single one.