In dealing with constrained multi-objective optimization problems (CMOPs), a key issue of multi-objective evolutionary algorithms (MOEAs) is to balance the convergence and diversity of working populations. However, most state-of-the-art MOEAs show poor performance in balancing them, and can easily cause the working populations to concentrate on a part of regions of the Pareto fronts, leading to a serious imbalanced searching between preserving diversity and achieving convergence. This paper proposes a method which combines a multi-objective to multi-objective (M2M) approach with the push and pull search (PPS) framework, namely PPS-M2M. To be more specific, the proposed algorithm decomposes a CMOP into a set of simple CMOPs. Each simple CMOP corresponds to a sub-population and is solved in a collaborative manner. When dealing with constraints, each sub-population follows a procedure of "ignore the constraints in the push stage and consider the constraints in the pull stage", which helps each working sub-population get across infeasible regions. In order to evaluate the performance of the proposed PPS-M2M, it is compared with the other six algorithms, including M2M, MOEA/D-Epsilon, MOEA/D-SR, MOEA/D-CDP, C-MOEA/D and NSGA-II-CDP on a set of benchmark CMOPs. The experimental results show that the PPS-M2M is significantly better than the other six algorithms.