Inter-algorithm cooperative approaches are increasingly gaining interest as a way to boost the search capabilities of evolutionary algorithms (EAs). However, the growing complexity of real-world optimization problems demands new cooperative designs that implement performance-driven strategies to improve the solution quality. This article explores multiobjective cooperation to address an important problem in bioinformatics: the reconstruction of phylogenetic histories from amino acid data. The proposed method is built using representative algorithms from the three main multiobjective design trends: 1) nondominated sorting genetic algorithm II; 2) indicator-based evolutionary algorithm; and 3) multiobjective evolutionary algorithm based on decomposition. The cooperation is supervised by an Elite island component that, along with managing migrations, retrieves multitrend performance feedback from each approach to run additional instantiations of the most satisfying algorithm in each stage of the execution. Experimentation on five real-world problem instances shows the benefits of the proposal to handle complex optimization tasks, in comparison to stand-alone algorithms, standard island models, and other state-of-the-art methods.