This paper introduces a unified estimation methodology using copulas for multivariate fractional outcomes with a conditional mean specification. These outcomes are defined as vectors where each component is bounded to the unit interval and together they add up to 1. The methods satisfy the fractional and unit-sum constraints while allowing for cross-equation restrictions among the conditional mean parameters, which are crucial in applications to structural estimation. While ultimately Bayesian in nature, the paper rigorously examines the asymptotic properties of the arising frequentist estimators, as they are themselves additions to the literature. The methodology is augmented to handle variable selection using regularization in a Bayesian framework. A range of numerical exercises evaluate the properties of the estimators and showcase their flexibility in examples of both structural and reduced form models. An empirical application to transportation expenditures in Canada is also presented.