  We study how the gravitational wave signal from stellar collapse in
scalar-tensor gravity varies under the influence of scalar self-interaction. To
this end, we extract the gravitational radiation from numerical simulations of
stellar collapse for a range of potentials with higher-order terms in addition
to the quadratic mass term. Our study includes collapse to neutron stars and
black holes and we find the strong inverse-chirp signals obtained for the
purely quadratic potential to be exceptionally robust under changes in the
potential at higher orders; quartic and sextic terms in the potential lead to
noticeable differences in the wave signal only if their contribution is
amplified, implying a relative fine-tuning to within 5 or more orders of
magnitude between the mass and self-interaction parameters.
