Bekenstein's tensor-vector-scalar (TeVeS) theory has had considerable success as a relativistic theory of modified Newtonian dynamics. However, recent work suggests that the dynamics of the theory are fundamentally flawed and numerous authors have subsequently begun to consider a generalization of TeVeS where the vector field is given by an Einstein-Æther action. Herein, I develop strong-field solutions of the generalized TeVeS theory, in particular exploring neutron stars as well as neutral and charged black holes. I find that the solutions are identical to the neutron star and black hole solutions of the original TeVeS theory, given a mapping between the parameters of the two theories, and hence provide constraints on these values of the coupling constants. I discuss the consequences of these results in detail including the stability of such spacetimes as well as generalizations to more complicated geometries.