  We study Proca stars in a vector-tensor gravity model inspired by Horndeski's
generalized Einstein-Maxwell field equations, supplemented with a mass term for
the vector field. We discuss the effects of the non-minimal coupling term on
the properties of the resulting Proca stars. %and show that they can form
vector hair. We show that the sign of the coupling constant is crucial in
determining the generic properties of these generalized Proca star solutions,
as soon as the magnitude of the coupling constant is sufficiently large to
allow for significant deviations from the standard Proca star case. For
negative coupling constant we observe a new type of limiting behavior for the
generalized Proca stars, where the spacetime splits into an interior region
with matter fields and an exterior Schwarzschild region.
