  We assess how much unused strong lensing information is available in the deep
\emph{Hubble Space Telescope} imaging and VLT/MUSE spectroscopy of the
\emph{Frontier Field} clusters. As a pilot study, we analyse galaxy cluster
MACS\,J0416.1-2403 ($z$$=$$0.397$, $M(R<200\,{\rm
kpc})$$=$$1.6$$\times$$10^{14}\msun$), which has 141 multiple images with
spectroscopic redshifts. We find that many additional parameters in a cluster
mass model can be constrained, and that adding even small amounts of extra
freedom to a model can dramatically improve its figures of merit. We use this
information to constrain the distribution of dark matter around cluster member
galaxies, simultaneously with the cluster's large-scale mass distribution. We
find tentative evidence that some galaxies' dark matter has surprisingly
similar ellipticity to their stars (unlike in the field, where it is more
spherical), but that its orientation is often misaligned. When non-coincident
dark matter and baryonic halos are allowed, the model improves by 35\%. This
technique may provide a new way to investigate the processes and timescales on
which dark matter is stripped from galaxies as they fall into a massive
cluster. Our preliminary conclusions will be made more robust by analysing the
remaining five \emph{Frontier Field} clusters.
