  We introduce a semi-parametric model for the primary mass distribution of
binary black holes (BBHs) observed with gravitational waves (GWs) that applies
a cubic-spline perturbation to a power law. We apply this model to the 46 BBHs
included in the second gravitational wave transient catalog (GWTC-2). The
spline perturbation model recovers a consistent primary mass distribution with
previous results, corroborating the existence of a peak at $35\,M_\odot$
($>97\%$ credibility) found with the \textsc{Powerlaw+Peak} model. The peak
could be the result pulsational pair-instability supernovae (PPISNe). The
spline perturbation model finds potential signs of additional features in the
primary mass distribution at lower masses similar to those previously reported
by Tiwari and Fairhurst (2021). However, with fluctuations due to small number
statistics, the simpler \textsc{Powerlaw+Peak} and \textsc{BrokenPowerlaw}
models are both still perfectly consistent with observations. Our
semi-parametric approach serves as a way to bridge the gap between parametric
and non-parametric models to more accurately measure the BBH mass distribution.
With larger catalogs we will be able to use this model to resolve possible
additional features that could be used to perform cosmological measurements,
and will build on our understanding of BBH formation, stellar evolution and
nuclear astrophysics.
