  We present a systematic investigation of the possible locations for the
special point (SP), a unique feature of hybrid neutron stars in the mass-radius
diagram. The study is performed within the two-phase approach where the
high-density (quark matter) phase is described by the covariant nonlocal
Nambu--Jona-Lasinio (nlNJL) model equation of state (EOS) which is shown to be
equivalent to a constant-sound-speed (CSS) EOS. For the nuclear matter phase
around saturation density different relativistic density functional EOSs are
used: DD2p00, its excluded-volume modification DD2p40 and the hypernuclear EOS
DD2Y-T. In the present contribution we apply the Maxwell construction scheme
for the deconfinement transition and demonstrate that a simultaneous variation
of the vector and diquark coupling constants results in the occurrence of SP
"trains" which are invariant against changing the nuclear matter EOS. We
propose that the SP train corresponding to a variation of the diquark coupling
at constant vector coupling is special since it serves as a lower bound for the
line of maximum masses and accessible radii of massive hybrid stars.
