We assess how much unused strong lensing information is available in the deep Hubble Space Telescope imaging and VLT/MUSE spectroscopy of the Frontier Field clusters . As a pilot study , we analyse galaxy cluster MACS J0416.1-2403 ( z = 0.397 , M ( R < 200 { kpc } ) = 1.6 \times 10 ^ { 14 } { M } _ { \sun } ) , 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 stellar 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 Frontier Field clusters .