  Gravitational wave observations of GW170817 placed bounds on the tidal
deformabilities of compact stars allowing one to probe equations of state for
matter at supranuclear densities. Here we design new parametrizations for
hybrid hadron-quark equations of state, that give rise to low-mass twin stars,
and test them against GW170817. We find that GW170817 is consistent with the
coalescence of a binary hybrid star--neutron star. We also test and find that
the I-Love-Q relations for hybrid stars in the third family agree with those
for purely hadronic and quark stars within $\sim 3\%$ for both slowly and
rapidly rotating configurations, implying that these relations can be used to
perform equation-of-state independent tests of general relativity and to break
degeneracies in gravitational waveforms for hybrid stars in the third family as
well.
