  Recent work has revealed that the light curves of hydrogen-poor (Type I)
superluminous supernovae (SLSNe), thought to be powered by magnetar central
engines, do not always follow the smooth decline predicted by a simple magnetar
spin-down model. Here we present the first systematic study of the prevalence
and properties of "bumps" in the post-peak light curves of 34 SLSNe. We find
that the majority (44-76%) of events cannot be explained by a smooth magnetar
model alone. We do not find any difference in supernova properties between
events with and without bumps. By fitting a simple Gaussian model to the
light-curve residuals, we characterize each bump with an amplitude,
temperature, phase, and duration. We find that most bumps correspond with an
increase in the photospheric temperature of the ejecta, although we do not see
drastic changes in spectroscopic features during the bump. We also find a
moderate correlation ($\rho\approx0.5$; $p\approx0.01$) between the phase of
the bumps and the rise time, implying that such bumps tend to happen at a
certain "evolutionary phase," $(3.7\pm1.4)t_\mathrm{rise}$. Most bumps are
consistent with having diffused from a central source of variable luminosity,
although sources further out in the ejecta are not excluded. With this
evidence, we explore whether the cause of these bumps is intrinsic to the
supernova (e.g., a variable central engine) or extrinsic (e.g., circumstellar
interaction). Both cases are plausible, requiring low-level variability in the
magnetar input luminosity, small decreases in the ejecta opacity, or a thin
circumstellar shell or disk.
