  Equation of state (EOS) insensitive relations, so-called universal relations,
between the neutron star (NS) compactness, its multipolar tidal deformability
coefficients, and between the tidal parameters for binary systems are essential
to break degeneracies in gravitational wave data analysis. Here, we validate
and recalibrate these universal relations using a large set of almost 2 million
phenomenological EOSs that are consistent with current observations. In doing
so, we extend universal relations to a larger region of the EOS parameter
space, most notably to softer EOSs and larger compactnesses. We show that
waveform models that neglect higher-than-leading-order tidal deformations of
the NSs accumulate as much as $3.5$ radians of dephasing from $20\,{\rm Hz}$ to
merger. We also perform a full Bayesian parameter estimation of the GW170817
data, and we compare the NS radius constraints produced using universal
relations from the literature and the updated fits we propose here. We find
that the new fits yield a NS radius that is smaller by about 500 meters. This
difference is less than the statistical uncertainty on the radius at the
signal-to-noise-ratio of GW170817, but it is significantly larger than the
precision anticipated for next-generation detectors.
