The traditional methods for synthesizing flexible heat exchanger networks (HENs) are not directly applicable to inter-plant HEN challenges, primarily due to the spread of system uncertainty across plants via intermedium fluid circles. This complicates the synthesis process significantly. To tackle this issue, this study proposes a decomposed stepwise methodology to facilitate the flexible synthesis of the inter-plant HENs performing indirect heat integration. A decomposition strategy is proposed to divide the overall network into manageable sub-networks by dissecting the intermedium fluid circles. To address the variability in intermedium fluid temperatures, a temperature fluctuation analysis approach is developed and a heuristic rule is introduced to maintain the temperature feasibility of the intermedium fluids. To ensure adequate flexibility and cost-effectiveness of the designed networks, flexibility analysis and network retrofit steps are conducted through model-based optimization techniques. The efficacy of the method is demonstrated through two case studies, showing its potential in achieving the desired operational flexibility for inter-plant HENs.