  We use 23 years of astrometric and radial velocity data on the orbit of the
star S0-2 to constrain a hypothetical intermediate-mass black hole orbiting the
massive black hole Sgr A* at the Galactic center. The data place upper limits
on variations of the orientation of the stellar orbit (inclination, nodal
angle, and pericenter) at levels between 0.02 and 0.07 degrees per year. We use
a combination of analytic estimates and full numerical integrations of the
orbit of S0-2 in the presence of a black-hole binary. For a companion IMBH
whose semi-major axis $a_c$ is larger than that of S0-2 (1020 a.u.), we find
that in the region between 1000 and 4000 a.u., a companion black hole with mass
$m_c$ between $10^3$ and $10^5 M_\odot$ is excluded, with a boundary behaving
as $a_c \sim m_c^{1/3}$. For a companion with $a_c < 1020$ a.u., we find that a
black hole with mass between $10^3$ and $10^5 \, M_\odot$ is again excluded,
with a boundary behaving as $a_c \sim m_c^{-1/2}$. These bounds arise from
quadrupolar perturbations of the orbit of S0-2. However, significantly stronger
bounds on the mass of an inner companion arise from the fact that the location
of S0-2 is measured relative to the bright emission of Sgr A*. As a
consequence, that separation is perturbed by the ``wobble'' of Sgr A* about the
center of mass between it and the companion, leading to ``apparent''
perturbations of S0-2's orbit that also include a dipole component. The result
is a set of bounds as small as $400 \, M_\odot$ at 200 a.u.; the numerical
simulations suggest a bound from these effects varying as $a_c \sim m_c^{-1}$.
We compare and contrast our results with those from a recent analysis by the
GRAVITY collaboration.
