Process capability indices (PCIs) have always been used to improve the quality of products and services. Traditional PCIs are based on the assumption that the data obtained from the quality characteristic (QC) under consideration are normally distributed. However, most data on manufacturing processes violate this assumption. Furthermore, the products and services of the manufacturing industry usually have more than one QC; these QCs are functionally correlated and, thus, should be evaluated together to evaluate the overall quality of a product. This study investigates and extends the existing multivariate non-normal PCIs. First, a multivariate non-normal PCI model from the literature is modeled and validated. An algorithm to generate non-normal multivariate data with the desired correlations is also modeled. Then, this model is extended using two different approaches that depend on the well-known Box−Cox and Johnson transformations. The skewness reduction is further improved by applying heuristics algorithms. These two approaches outperform the investigated model from the literature because they can provide more precise results regardless of the skewness type. The comparison is made based on the generated data and a case study from the literature.