  We give the Lagrangian formulation of a generic non-minimally extended
Einstein-Maxwell theory with an action that is linear in the curvature and
quadratic in the electromagnetic field. We derive the coupled field equations
by a first order variational principle using the method of Lagrange
multipliers. We look for solutions describing plane-fronted Einstein-Maxwell
waves with parallel rays. We give a family of exact solutions associated with a
partially massless spin-2 photon and a partially massive spin-2 graviton.
