  Based on the rate of change of its orbital period, PSR J2043+1711 has a
substantial peculiar acceleration of 3.5 $\pm$ 0.8 mm/s/yr, which deviates from
the acceleration predicted by equilibrium Milky Way models at a $4\sigma$
level. The magnitude of the peculiar acceleration is too large to be explained
by disequilibrium effects of the Milky Way interacting with orbiting dwarf
galaxies ($\sim$1 mm/s/yr), and too small to be caused by period variations due
to the pulsar being a redback. We identify and examine two plausible causes for
the anomalous acceleration: a stellar flyby, and a long-period orbital
companion. We identify a main-sequence star in \textit{Gaia} DR3 and Pan-STARRS
DR2 with the correct mass, distance, and on-sky position to potentially explain
the observed peculiar acceleration. However, the star and the pulsar system
have substantially different proper motions, indicating that they are not
gravitationally bound. However, it is possible that this is an unrelated star
that just happens to be located near J2043+1711 along our line of sight (chance
probability of 1.6\%). Therefore, we also constrain possible orbital parameters
for a circumbinary companion in a hierarchical triple system with J2043+1711;
the changes in the spindown rate of the pulsar are consistent with an outer
object that has an orbital period of 80 kyr, a companion mass of 0.3 $M_\odot$
(indicative of a white dwarf or low-mass star), and a semi-major axis of 2000
AU. Continued timing and/or future faint optical observations of J2043+1711 may
eventually allow us to differentiate between these scenarios.
