Yup. Been using Clearly Natural glycerin bar soap for years. Used to be a buck a bar at the Dollar Store, but now the price has doubled! (On Amazon, at least)Perhaps just use a bar of glycerine soap as a base puck for your soap or cream in your shaving mug? Various brands are sold at grocery stores and pharmacies, and they are not expensive.
Works great, for me, without additional soap or cream.