The Hospitals/Residents with Ties problem (HRT) can yield stable matchings of varying sizes. A well-known NP-hard task is to find a stable matching of maximal size in any HRT situation, known as MAX-HRT. In this study, we report a heuristic search strategy designed specifically to tackle MAX-HRT. First, we randomly assign residents to hospitals. Next, we solve one undominated blocking pair at a time until we find the best solution, iteratively improving this assignment. We conduct a series of experiments to assess the performance of our algorithm against adaptive search techniques and hospital-proposing methods. Results indicate that our strategy provides improved efficiency in terms of both execution time and solution quality, especially when working with large-scale MAX-HRT instances.