  Current searches for signals of departures from the fundamental symmetries of
General Relativity using gravitational waves are largely dominated by
propagation effects like dispersion and birefringence from highly dynamic
sources such as coalescing binary-black holes and neutron stars. In this paper
we take steps towards probing the nature of spacetime symmetries in the {\it
generation-stage} of gravitational waves; by using a generic effective-field
theory, we solve the modified Einstein equations order-by-order (in the
coefficients for the symmetry breaking) for a generic source, and we write down
the the first Post-Newtonian corrections, which includes contributions from the
spacetime-symmetry breaking terms. Choosing as the source a system of point
particles allows us to write down a simple toy solution explicitly, and we see
that in contrast to General Relativity, the monopolar and dipolar contributions
are non-vanishing. We comment on the detectability of such signals by the Laser
Interferometer Space Antenna (LISA) space mission, which has high
signal-to-noise galactic binaries (which can be modelled as point particles)
well inside its predicted sensitivity band, sources which are inaccessible for
current ground-based detectors, and we also discuss the possibility of going
beyond the quadrupole formula and the first Post-Newtonian order, which would
reveal effects which could be probed by ground-based detectors observing
coalescence events.
