In this paper, a new type of Multi-Objective Problems (MOPS) is introduced and formulated. The new type is an outcome of a motivation to find optimal solutions for different MOPs, which are coupled through communal components. Therefore, in such cases a multi-Multi-Objective Optimization Problem (m-MOOP) has to be considered. The solution to the m-MOOP is defined and an approach to search for it by applying an EMO algorithm sequentially is presented. This method, although not always resulting in the individual MOPS' Pareto fronts, nevertheless gives solutions to the m-MOOP problem in hand. Several measures that allow the assessment of the introduced approach are offered. To demonstrate the approach and its applicability, academic examples as well as a "real-life," engineering example, are given.