Epistasis and NK-Landscapes in the context of multiobjective evolutionary algorithms (MOEAs) are almost unexplored subjects. We have presented an extension of Kauffman's NK-Landscapes to multiobjective MNK-Landscapes and gave some insights into their properties from a multiobjective standpoint. These properties allow us to meaningfully use MNK-Landscapes as a benchmark tool and as a means to understand better the working principles of MOEAs. In this work we present four multiobjective random bit climbers (moRBCs) and use them to study the effects or elitism and population climbing on scalable random epistatic problems. Each moRBC implements a different kind of elitism in order to understand better its working principles. We conduct experiments on MNK-Landscapes with M = {2, 3, 5} objectives, N = 100 bits, varying the epistatic interactions K from 0 to 50. Results by an elitist non-dominated sorting multiobjective genetic algorithm (NSGA-II) are also included for comparison.