Should a stereo soundstage be 3D or 2D?

I read several people talking about a “3D” soundstage. The main purpose of stereo is to provide left-right separation between different sounds in a recording (a “wide” soundstage). I understand that when properly set up, there is also front-back separation (a “deep” soundstage). So there are certainly two dimensions. Where is the third? Will a stereo system provide up-down separation as well? What is the technical explanation?

Thanks for the help!