More uniform provision of information for univariate and multivariate quantities

For a multivariate quantity, there are cases where one is interested only in the covariance matrix and not in any coverage region. For example, from a calibration one may be interested in the coefficients of the calibration model and their associated covariance matrix. From a practical point of view, coverage regions for such an example do not really make sense.

For the univariate case, we allow the provision either of an (expanded) uncertainty or a coverage interval. For a multivariate region, can we similarly allow the provision either of a covariance matrix or a coverage region?