Imported STEP Assemblies Saved As Solidworks Assemblies

We often get large assemblies from our customers, usually in STEP format. When I import into SW I get a bunch of "Imported" bodies for the individual parts but when I try to save it as a SW assembly it doesn't work.

My workaround so far (and yes, it's ok to laugh at me, I'm laughing too. Kind of.) is to toss what I don't really need, save the file as a separate name and delete everything else that is NOT the part I want to keep. Then I save that as a new file and go back to the assembly and do it over again for the next part. If I really need the assy in tact after that point I will have to rebuild it.

TYIA.

SolidworksAssemblies