  We present new spatially resolved astrometry and photometry of the CD-27
11535 system, a member of the $\beta$ Pictoris moving group consisting of two
resolved K-type stars on a $\sim$20-year orbit. We fit an orbit to relative
astrometry measured from NIRC2, GPI, and archival NaCo images, in addition to
literature measurements. However, the total mass inferred from this orbit is
significantly discrepant from that inferred from stellar evolutionary models
using the luminosity of the two stars. We explore two hypotheses that could
explain this discrepant mass sum; a discrepant parallax measurement from Gaia
due to variability, and the presence of an additional unresolved companion to
one of the two components. We find that the $\sim$20-year orbit could not bias
the parallax measurement, but that variability of the components could produce
a large amplitude astrometric motion, an effect which cannot be quantified
exactly without the individual Gaia measurements. The discrepancy could also be
explained by an additional star in the system. We jointly fit the astrometric
and photometric measurements of the system to test different binary and triple
architectures for the system. Depending on the set of evolutionary models used,
we find an improved goodness of fit for a triple system architecture that
includes a low-mass ($M=0.177\pm0.055$\,$M_{\odot}$) companion to the primary
star. Further studies of this system will be required in order to resolve this
discrepancy, either by refining the parallax measurement with a more complex
treatment of variability-induced astrometric motion, or by detecting a third
companion.
