Synthesis of Heat Exchanger Networks (HENs) is widely recognized as one of the most energy-saving techniques in the process industry. However, most existing HEN synthesis methods and intentions concentrate only on solving the problems of fixed process stream data, which means for a certain network, things would get worse or even infeasible when operating conditions such as stream input temperature and flowrate vary in practice. It is of great significance to ensure the designed HENs having adequate competence to tolerate the fluctuations in operating conditions, which is called flexibility. This paper presents a stepwise methodology to perform flexible inter-plant HENs synthesis, especially for the indirect heat integration involving intermediate fluid circles. The flexible synthesis step is based on the flexible analysis of an initial network. To improve the flexibility of the entire system, a new strategy is proposed, that is additional utility heat exchangers are introduced not only into each intra-plant HEN but also on intermediate fluid circles for the sake of utilizing the broad relevance of the circles. So in the work, the temperature, network structure, heat exchanger area and the location to place additional equipment are all optimized. An improved design that can tolerate fluctuations with lower total annual cost (TAC) can be found by using this methodology. Finally, a case study is presented to demonstrate the proposed method, and the results have confirmed the effectiveness and feasibility.