The BPS Skyrme model is a specific subclass of Skyrme-type field theories which possesses both a BPS bound and infinitely many soliton solutions (skyrmions) saturating that bound. A related property, the existence of a large group of symmetry transformations, allows for solutions of rather general shapes, which is in contrast to the situation for the original Skyrme model, where soliton solutions usually have some fixed shapes. We study here the classical symmetries of the BPS Skyrme model, applying them to construct soliton solutions with some prescribed shapes, which constitutes a further step to understand the similarities and differences with the original Skyrme model.