As Internet of Things (IoT) applications expand, Mobile Edge Computing (MEC) has emerged as a promising architecture to overcome the real-time processing limitations of mobile devices. Edge-side computation offloading plays a pivotal role in MEC performance but remains challenging due to complex task topologies, conflicting objectives, and limited resources. This paper addresses high-dimensional multi-objective offloading for serial heterogeneous tasks in MEC. We jointly consider task heterogeneity, high-dimensional objectives, and flexible resource scheduling, modeling the problem as a Many-objective optimization. To solve it, we propose a flexible framework integrating an improved cooperative co-evolutionary algorithm based on decomposition (MOCC/D) and a flexible scheduling strategy. Experimental results on benchmark functions and simulation scenarios show that the proposed method outperforms existing approaches in both convergence and solution quality.