The talk reports on recent progress in amplitude computations for broad classes of $N=2$ Maxwell-Einstein and Yang-Mills-Einstein supergravities, using the framework provided by color/kinematics duality and the double-copy construction.

After a review of the main theoretical tools, we discuss the extension of the double-copy construction to a particular infinite family of $N=2$ Maxwell-Einstein theories in four and five dimensions, the so-called generic Jordan family of supergravities.

We show that the global symmetries of these theories can easily be gauged, giving the amplitudes of the corresponding Yang-Mills-Einstein supergravities. We also discuss how the construction can be modified to describe spontaneous symmetry breaking. Finally, we present an extension of the construction that captures an even larger class of $N=2$ homogeneous supergravities.