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 $\ensuremath{\gtrsim}2.05\phantom{\rule{0.16em}{0ex}}{\mathrm{M}}_{\mathrm{Sun}}$, while being in good agreement with gravitational-wave events and x-ray pulsar observations, when quark vector interactions and nonstandard 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 $2.5\phantom{\rule{0.16em}{0ex}}{\mathrm{M}}_{\mathrm{Sun}}$. 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 nonrotating stars. This is not the case for pure quark stars, which can easily reach $2.5\phantom{\rule{0.16em}{0ex}}{\mathrm{M}}_{\mathrm{Sun}}$ and still possess approximately the same amount of baryons as stable nonrotating 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.