Blender Export to Multiple Parts
Batch Export of OBJ
Blender can export an STL or OBJ as multiple parts - by using a plugin.
- There is a plugin to export a batch of parts as individual files in Blender. 
- More info on multiple part export from last link 
- Link to Blender add-on at 
- Note - see the comment on Blender 2.8 - where you apparently need to use a modified version of the addon if you are at Blender 2.8x and not higher.
- MJ comment - the 2.8 script worked on OSE Linux 2.0 Prerelease on 2/8/21.
- But - how to import as multiple OBJ files from SweetHome3D?
OBJ batch also works for import.
You can apply the same scaling to multiple objects in Blender by selecting all of them, ans as you type the scale number, hold Alt (once you start editing the value). When you press return, while holding down Alt, the scale will be applied to all the objects. 
How to Export Sweet Home into Multiple Parts
No evidence that this can be done. Question to SweetHome3D Forum:
Is there any way to export a SweetHome3D design as individual OBJ files? I'm trying to import into Blender while retaining individual parts, and Blender has the capacity to open up a batch of OBJ files at one time. This is an issue that arises from my need to scale SweetHome3D content 10x when importing to FreeCAD to retain the correct scale. It's a 10x factor.
Also - my suggestion is to fix the 10x scaling factor between SweetHome3D and FreeCAD export. That way objects from SweetHome can be used right in FreeCAD, and FreeCAD exports could be used directly in SweetHome. I just found that 3D Videos in SweetHome can be used to make excellent animations for exported FreeCAD content - the ability to make a ready walk-through animation out of FreeCAD work was the easiest walk-through animation workflow I've ever seen - great job Emmanuel.
Any other suggestions on workaround are welcome.
After More Looking
I found a plugin for SweetHome3D which privides exactly the export of SH3D into Blender as needed as an XML file. See Blender Import of Multiple Parts for details - SH3D info is there as well.