  The variety of consistent "gauging" deformations of supergravity theories in
four dimensions depends on the choice of Lagrangian formulation. One important
goal is to get the most general deformations without making hidden assumptions.
Ignoring supersymmetry we consider in this paper $n_v$ abelian vector
potentials in four spacetime dimensions with non-minimal kinetic coupling to
$n_s$ uncharged (possibly nonlinear) scalar fields. As in the case of extended
supergravities, one model may possess different formulations related by
$Sp(2n_v,\mathbb{R})$. The symplectic group mixes its electric and magnetic
potentials. The model admits a global duality symmetry subgroup $G$ which acts
also on the scalars. We recall first how the general second order Lagrangian,
its local deformations and those of its abelian gauge group will depend on the
choice of $2n_v$ directions (choice of "Darboux frame"). We start from a
general frame defined by the symplectic transformation relating it to a
fixed"reference" one. Combinations of symplectic matrix coefficients appear
then as constant parameters in the second order Lagrangians. Another gauging
method uses an "embedding tensor" that characterizes the realization of the
gauge group via the global duality group. It involves additional 2-form gauge
fields. A suitable zero charge limit of this realization has abelian gauge
group and the "gauging" can be viewed as a consistent deformation of that
limit. We show that the two methods applied to the corresponding ungauged
models have equivalent local deformations -- and more generally, have
isomorphic local BRST cohomology at all ghost numbers. We finally consider
manifestly duality invariant first order actions with abelian gauge group. We
point out that obstructions to non-abelian deformations of the Yang-Mills type
exhibited in a previous work remain present when couplings to scalar fields are
included.
