Dragging it and dropping it doesnt work.
Add the original prefab into the scene, add the new prefab as a child to it, then drag the original prefab back onto the prefab in the project view (or just click Apply in the inspector)
Probably want to delete it from the scene after that
You're not going to be able to make a prefab a child of another prefab in the sense that they're still connected. Unity doesn't support "nested" prefabs like that.
You can do like Mike suggested, whereas you make a prefab that results in the combination of prefab A and prefab B, but if you change your original prefab that's the child object, you're not going to see the changes propagated to the parent+child prefab.
One way to work around this is to set up a variable on a script somewhere that takes a prefab (GameObject) parameter, and instantiate it at run time.
And if you want to keep the connection between a prefab and its prefabs children you need the nested prefabs feature.
This feature is not yet available in Unity but I have developed an Editor Extension that allows you to do that:
http://u3d.as/content/bento-studio/nested-prefab/2Jz
Hope this helps.