  We extend the recently developed hybrid quark-meson-nucleon model by
augmenting a six-point scalar interaction and investigate the consequences for
neutron-star sequences in the mass-radius diagram. The model has the
characteristic feature that, at increasing baryon density, the chiral symmetry
is restored within the hadronic phase by lifting the mass splitting between
chiral partner states (parity doubling), before quark deconfinement takes
place. At low temperature and finite baryon density, the model predicts a
first-, second-order chiral phase transition, or a crossover, depending on the
expectation value of the scalar field, and a first-order deconfinement phase
transition. We discuss two sets of free parameters, which result in
compact-star mass-radius relations that are at tension with the combined
constraints for maximum-mass ($2~M_\odot$) and the compactness (GW170817). We
find that the most preferable mass-radius relations result in isospin-symmetric
phase diagram with rather low temperature for the critical point of the chiral
phase transition.
