Artificial intelligence (AI) systems in healthcare have demonstrated remarkable potential to improve patient outcomes. However, if not designed with fairness in mind, they also carry the risks of perpetuating or exacerbating existing health disparities. Although numerous fairness-enhancing techniques have been proposed, most focus on a single sensitive attribute and neglect the broader impact that optimizing fairness for one attribute may have on the fairness of other sensitive attributes. In this work, we introduce a novel approach to multi-attribute fairness optimization in healthcare AI, tackling fairness concerns across multiple demographic attributes concurrently. Our method follows a two-phase approach: initially optimizing for predictive performance, followed by fine-tuning to achieve fairness across multiple sensitive attributes. We develop our proposed method using two strategies, sequential and simultaneous. Our results show a significant reduction in Equalized Odds Disparity (EOD) for multiple attributes, while maintaining high predictive accuracy. Notably, we demonstrate that single-attribute fairness methods can inadvertently increase disparities in non-targeted attributes whereas simultaneous multi-attribute optimization achieves more balanced fairness improvements across all attributes. These findings highlight the importance of comprehensive fairness strategies in healthcare AI and offer promising directions for future research in this critical area.