In manufacturing industries, it is often seen that the bilateral specification limits corresponding to a particular quality characteristic are not symmetric with respect to the stipulated target. A unified superstructure C p ′ ′ ( u , v ) of univariate process capability indices was specially designed for processes with asymmetric specification limits. However, as in most of the practical situations a process consists of a number of inter‐related quality characteristics, subsequently, a multivariate analogue of C p ′ ′ ( u , v ) , which is called C M ( u , v ), was developed. In the present paper, we study some properties of C M ( u , v ) like threshold value and compatibility with the asymmetry in loss function. We also discuss estimation procedures for plug‐in estimators of some of the member indices of C M ( u , v ). Finally, the superstructure is applied to a numerical example to supplement the theory developed in this article.