Intersectional fairness is a critical requirement for Machine Learning (ML) software, demanding fairness across subgroups defined by multiple protected attributes. This paper introduces FairHOME, a novel ensemble approach using higher order mutation of inputs to enhance intersectional fairness of ML software during the inference phase. Inspired by social science theories highlighting the benefits of diversity, FairHOME generates mutants representing diverse subgroups for each input instance, thus broadening the array of perspectives to foster a fairer decision-making process. Unlike conventional ensemble methods that combine predictions made by different models, FairHOME combines predictions for the original input and its mutants, all generated by the same ML model, to reach a final decision. Notably, FairHOME is even applicable to deployed ML software as it bypasses the need for training new models. We extensively evaluate FairHOME against seven state-of-the-art fairness improvement methods across 24 decision-making tasks using widely adopted metrics. FairHOME consistently outperforms existing methods across all metrics considered. On average, it enhances intersectional fairness by 47.5%, surpassing the currently best-performing method by 9.6 percentage points.