Welcome to SolidWorks forums Shai.
I don't see there is direct way to do that but here is a work around you can try:
- Convert you multi body to assembly (just on few mouse clicks): Assembly from Part – No mates required
- Now save your assembly as STL and make sure this option is unchecked: Save all components of an assembly in a single file
The other way might be to make a macro to do it all automatic
You might also find this post helpful for your future reference.
Please use "advanced editor" in case you want to attach any files.
Thank you very much
very very helpfull