In the standard use case of Algorithmic Fairness, the goal is to eliminate the relationship between a sensitive variable and a corresponding score. Throughout recent years, the scientific community has developed a host of definitions and tools to solve this task, which work well in many practical applications. However, the applicability and effectivity of these tools and definitions becomes less straightfoward in the case of multiple sensitive attributes. To tackle this issue, we propose a sequential framework, which allows to progressively achieve fairness across a set of sensitive features. We accomplish this by leveraging multi-marginal Wasserstein barycenters, which extends the standard notion of Strong Demographic Parity to the case with multiple sensitive characteristics. This method also provides a closed-form solution for the optimal, sequentially fair predictor, permitting a clear interpretation of inter-sensitive feature correlations. Our approach seamlessly extends to approximate fairness, enveloping a framework accommodating the trade-off between risk and unfairness. This extension permits a targeted prioritization of fairness improvements for a specific attribute within a set of sensitive attributes, allowing for a case specific adaptation. A data-driven estimation procedure for the derived solution is developed, and comprehensive numerical experiments are conducted on both synthetic and real datasets. Our empirical findings decisively underscore the practical efficacy of our post-processing approach in fostering fair decision-making.