  We consider the case of several scalar fields, charged under a number of U(1)
factors, acquiring vacuum expectation values due to an anomalous U(1). We
demonstrate how to make redefinitions at the superfield level in order to
account for tree-level exchange of vector supermultiplets in the effective
supergravity theory of the light fields in the supersymmetric vacuum phase. Our
approach builds upon previous results that we obtained in a more elementary
case. We find that the modular weights of light fields are typically shifted
from their original values, allowing an interpretation in terms of the
preservation of modular invariance in the effective theory. We address various
subtleties in defining unitary gauge that are associated with the noncanonical
Kahler potential of modular invariant supergravity, the vacuum degeneracy, and
the role of the dilaton field. We discuss the effective superpotential for the
light fields and note how proton decay operators may be obtained when the heavy
fields are integrated out of the theory at the tree-level. We also address how
our formalism may be extended to describe the generalized Green-Schwarz
mechanism for multiple anomalous U(1)'s that occur in four-dimensional Type I
and Type IIB string constructions.
