The "no-hair" theorem can, in principle, be tested at the center of the Milky
Way by measuring the spin and the quadrupole moment of Sgr A${}^{\ast}$ with the
orbital precession of S-stars, measured over their full periods. Contrary to
the original method, we show why it is possible to test the no-hair theorem
using observations from only a single star, by measuring precession angles over
a half-orbit. There are observational and theoretical reasons to expect S-stars
to spin rapidly, and we have quantified the effect of stellar spin, via
spin-curvature coupling (the leading-order manifestation of the
Mathisson-Papapetrou-Dixon equations), on future quadrupole measurements. We
find that they will typically suffer from errors of order a few percentage
points, but for some orbital parameters, the error can be much higher. We
re-examine the more general problem of astrophysical noise sources that may
impede future quadrupole measurements, and find that a judicious choice of
measurable precession angles can often eliminate individual noise sources. We
have derived optimal combinations of observables to eliminate the large noise
source of mass precession, the novel noise of spin-curvature coupling due to
stellar spin, and the more complicated noise source arising from transient
quadrupole moments in the stellar potential.