Is there a way to export a multi-part prop in OBJ form, specifically a complicated building interior, and after removing unwanted portions such as an exterior wall re-import the prop with its remaining parts identified? I have sometimes succeeded but all too often the mutilated scene comes back as a whole piece without parts.

Assuming that you're using a modelling app like Hexagon or Wings3d
to remove the parts ..... it sounds like the modelling app is misnaming
the groups or is mashing everything together as one group.

If you're only wanting to remove pieces "by name", Poser's grouping
tool will do the job more easily. 

If the pieces are groups, the grouping tool can delete an entire group. 
If they are set up as material zones:  hit "New Group", then "Add material",
and pick the desired material.  Then you can delete this group.

Another option in the grouping tool:  Start by hitting "Spawn Props",
then delete the original item.  You'll then have a separate prop from
each piece that was originally a body part or group.  You can delete
the props you don't want.  Then you can re-export the remainder as OBJ
or just use it this way as separate props.
hit the

Second thought:  Are you sure you're not checking the "Export as Single Group"
box when you export?

Well, this is very interesting  but I'm still stuck. I'm using Ray Dream Studio. I notice I was exporting as a "Single Frame" (it has sometimes worked) but multi-frame exporting doesn't help. I'll try the grouping tool, but either way many thanks for your considerate help.