Numerous design methods for the retrofit of heat exchanger networks have been proposed over the years, with most depending greatly on topology modification and additional heat transfer area. However, topology modifications and the installation of additional heat transfer area can lead to uneconomic retrofit in many cases, largely as a result of the expense of civil engineering work and pipework modifications. Retrofit of a heat exchanger network can be achieved without the need for topology modifications and additional heat transfer area by the use of heat transfer enhancement. This paper presents a methodology for heat exchanger network retrofit around a fixed network and without the need for additional heat transfer area and topology modifications. Heat transfer enhancement techniques are used to improve the energy performance of an existing heat exchanger network. A dominance ratio is explored to identify the best location to apply enhancement. Sensitivity analysis is used in finding the sequence of the most effective heat exchangers to enhance in order to improve the performance of the network. Sensitivity analysis introduced to study network flexibility is adapted to study heat transfer enhancement. Heat exchanger networks are complex systems with interactions between various components. A change in one component can have an effect on other downstream heat exchangers. Therefore, the proposed methodology presents a way of eliminating the need for additional heat transfer area after enhancement, while ensuring the stream target temperatures are met. This is based on a key optimisation strategy which depends on a trade-off between utility consumption and the need for additional heat transfer area.