It has worked on every soap I have tried it on. It is after all how milled soaps are made. Triple milled soaps have gone through this process three times.
So called glycrine soaps (the ones that are clear or at least mostly transparent) have also gone through this process, but with the added step of being rebatched with alcohol.
There is really no such thing as a glycerine based soap, glycerine is produced during soap making and can also be added as an extra ingredient, but all soaps are fat based.