  There are a subset of short gamma-ray bursts (SGRBs) which exhibit a
rebrightening in their high-energy light curves known as extended emission.
These bursts have the potential to discern between various models proposed to
describe SGRBs as any model needs to account for extended emission. In this
paper, we combine fallback accretion into the magnetar propeller model and
investigate the morphological changes fallback accretion has on model light
curves and fit to the afterglows of 15 SGRBs exhibiting extended emission from
the Swift archive. We have parameterised the fallback in terms of existing
parameters within the propeller model and solved for the disc mass and angular
frequency of the magnetar over time. We then apply a Markov chain Monte Carlo
routine to produce fits to the data. We present fits to our extended emission
SGRB sample that are morphologically and energetically consistent with the data
provided by Swift BAT and XRT telescopes. The parameters derived from these
fits are consistent with predictions for magnetar properties and fallback
accretion models. Fallback accretion provides a noticeable improvement to the
fits of the light curves of SGRBs with extended emission when compared to
previous work and could play an important role in explaining features such as
variability, flares and long dipole plateaux.
