Improper rotation is also called rotation-reflection or rotoreflection (along with some other names). Biological macromolecules generally can’t have reflection symmetries, because they are strictly chiral.
Can you provide some more information about your complex? You may have a non-point group symmetry, which can still be treated using local expansion methods from a few different software packages. CryoSPARC can still be used for refinement after importing transformed particles. This approach will also work if you have a true S4 symmetry (of a non-biological sample).
@mmclean Just FYI RELION actually has S symmetries. I guess someone over there is a completionist…