This talk presents a recent effort to develop a parametrised “post-GR”
framework for modelling non-rotating relativistic stars without adhering
to any particular alternative theory of gravity. The resulting “post-TOV”
formalism comprises equations for the stellar interior and exterior that
deviate from the general relativistic ones by the addition of compact
parametrised post-Newtonian terms. We discuss a number of interesting
astrophysical applications of the post-TOV toolkit together with the prospect
of constraining possible deviations from GR. We conclude by giving some
pointers on future improvements of the formalism.