I just use the right-click menus for that. First you create a new surface, then you select things and put them into the new surface.
When the Geometry Editor cursor is over the 3D item, right-click and then...
Geometry Assignment > Create Surface > [type in a name]
Start the name with 0 (zero) so it will be at the top of the list, like "0_Example"
Now you'll see 0_Example in the Surfaces tab.
Select an area, then right-click again...
Geometry Assignment > Assign To Surface > 0_Example
All of those pieces are moved out of their original surface and into the new one. Then you can turn the opacity of the new surface down to zero, or make any other changes you want.
This all sticks if you save as a complete scene. Good luck!