Energy conservation and emission reduction have become critical issues due to increasing environmental policy pressures and high energy prices. Work and heat exchange network (WHEN) synthesis is a promising approach to enhance the energy efficiency of energy-intensive processes. WHEN considering single-stage compression/expansion can be divided into two classes by structure complexity: minimal structure and non-minimal structure. The synthesis problem of minimal structure has been addressed in our previous work, where the global optimal solution can be guaranteed. In contrast, the compressors/expanders are not at the beginning or end of the streams' paths in the non-minimal structure and therefore the inlet/outlet temperatures are now variables of the problem. Instead of solving this complicated problem directly, we propose a super-targeting model to screen and scope the solution space for primal promising options before detailed structure design which can be designed using regular HEN synthesis methods. The super-target is estimated by regulating the thermodynamic paths of hot and cold streams where the objective function uses classical HEN super-target to evaluate the costs of the heat exchanger network. Benefiting from the unimodal nature of non-minimal WHEN super-targeting problems, we develop two deterministic algorithms: one relies on derivatives and one is derivative-free. Case studies show the efficiency of the proposed algorithm. The resulting TAC can be 23.1% lower than the literature report and the solution of super-targeting problems are proven to be globally optimal. The derivative optimization algorithm has been found to exhibit superior efficiency in solving problems of relatively large scale.