  In the context of the massive secondary object recently observed in the
compact-star merger GW190814, we investigate the possibility of producing
massive neutron stars from a few different equation of state models that
contain exotic degrees of freedom, such as hyperons and quarks. Our work shows
that state-of-the-art relativistic mean field models can generate massive stars
reaching $\gtrsim 2.05\,\Msun$, while being in good agreement with
gravitational-wave events and x-ray pulsar observations, when quark vector
interactions and non-standard self-vector interactions are introduced. In
particular, we present a new version of the Chiral Mean Field (CMF) model in
which a different quark-deconfinement potential allows for stable stars with a
pure quark core. When rapid rotation is considered, our models generate stellar
masses that approach, and in some cases surpass $2.5\,\Msun$. We find that in
such cases fast rotation does not necessarily suppress exotic degrees of
freedom due to changes in stellar central density, but require a larger amount
of baryons than what is allowed in the non-rotating stars. This is not the case
for pure quark stars, which can easily reach $2.5\,\Msun$ and still possess
approximately the same amount of baryons as stable non-rotating stars. We also
briefly discuss possible origins for fast rotating stars with a large amount of
baryons and their stability, showing how the event GW190814 can be associated
with a star containing quarks as one of its progenitors.
