  The detection of an unexpected $\sim 2.5 M_{\odot}$ component in the
gravitational wave event GW190814 has puzzled the community of High-Energy
astrophysicists, since in the absence of further information it is not clear
whether this is the heaviest "neutron star" ever detected or either the
lightest black hole known, of a kind absent in the local neighbourhood. We show
in this work a few possibilities for a model of the former, in the framework of
three different quark matter models with and without anisotropy in the interior
pressure. As representatives of classes of "exotic" solutions, we show that
even though the stellar sequences may reach this ballpark, it is difficult to
fulfill simultaneously the constraint of the radius as measured by the NICER
team for the pulsar PSR J0030+0451. Thus, and assuming both measurements stand,
compact neutron stars can not be all made of self-bound quark matter, even
within anisotropic solutions which boost the maximum mass well above the $\sim
2.5 M_{\odot}$ figure. We also point out that a very massive compact star will
limit the absolute maximum matter density in the present Universe to be less
than 6 times the nuclear saturation value.
