We start with two examples where polymorphs exist with the same space group symmetry, so that a transformation between their corresponding local energy minima should be possible with space group symmetry constrained, i.e. Monte Carlo moves are only allowed which maintain the original symmetry. This is performed by perturbing the asymmetric unit of the crystal structure and applying symmetry-related perturbations to all other molecules in the unit cell. Constraints are also applied to unit cell parameters, where these are required to maintain space group symmetry.