Analytical target cascading (ATC) is a hierarchical multilevel multidisciplinary design methodology. In ATC, top level design targets (i.e., specifications) are propagated to lower level design problems in a consistent and efficient manner. In this article, a modified Lagrangian dual formulation and coordination for ATC are developed to enhance a formulation and coordination proposed earlier in the literature. The proposed approach guarantees all the properties established earlier but additionally offers new significant advantages. As established before for the convex case, the proposed ATC coordination converges to a global optimal solution with corresponding optimal Lagrange multipliers in the dual space. The Lagrange multipliers can be viewed as the weights for deviations in ATC formulations. Thus the proposed coordination algorithm finds the optimal solution and the optimal weights for the deviation terms simultaneously. The enhancement allows for target cascading between levels, the use of augmented Lagrangian to improve convergence of the coordination algorithm, and for prevention from unboundedness. A guideline to set the step size for subgradient optimization when solving the Lagrangian dual problem is also proposed.