Many optimisation problems have more than three objectives, referred to as many-objective optimisation problems (MaOPs). As the number of objectives increases, the number of solutions that are non-dominated with regards to one another also increases. Therefore, multi-objective optimisation algorithms (MOAs) that use Pareto-dominance struggle to converge to the Pareto-optimal front (POF) and to find a diverse set of solutions on the POF. This article investigates the use of MOAs to solve MaOPs by guiding the search through Pareto-dominance on three randomly selected objectives. This approach is applied to the non-dominated sorting genetic algorithm II (NSGA-II) and a multi-objective particle swarm optimisation (OMOPSO) algorithm, where three objectives are randomly selected at either every iteration or every five iterations. These algorithms are compared against the original versions of these algorithms. The results indicate that the proposed partial dominance approach outperformed the original versions of these algorithms, especially on benchmarks with 8 and 10 objectives.