  It has been known for some time that compact stars containing quark matter
can masquerade as neutron stars in the range of measured mass and radius,
making it difficult to draw firm conclusions on the phases of matter present
inside the star. Using the vector-enhanced Bag model (vBag), we examine
mass-radius and mass-compactness relations with Maxwell and Gibbs construction
for hybrid stars with transitions from nuclear matter to two or three-flavor
quark matter, including sequential transitions. Not only can stable hybrid
stars with either two or three-flavor quark matter mimic neutron stars (the
traditional masquerade), it appears as well difficult to distinguish two-flavor
from three-flavor quark matter even in cases where a phase transition can be
said to have occurred, as in the presence of a distinct kink in the mass-radius
relation. Furthermore, allowing for sequential flavor transitions, we find that
the transition into an unstable branch can be caused by either a transition
from a nuclear to unstable quark matter or the sequential transition from
nuclear to stable but "masquerading" two-flavor to unstable three-flavor quark
matter. Addressing chiral restoration as well as quark deconfinement in a model
of the phase transition, as the vBag does, adds further flexibility to the
high-density equation of state, motivating caution in using even high-precision
$M$-$R$ data to draw firm conclusions on the nature of phases and phase
transitions in neutron stars.
