I often want to do this but can't. I have to copy design to a Library folder and then manually move the files to a Projects folder.
Our VAR setup Vault Basic with Library.ipj and Projects.ipj which we are happy with. All files in Library are made and locked away (or I wish they were but that is another topic). But we are constantly adding items to the Library either as new or as copy design.
We have a similar need because we have template assemblies for tooling design on different pieces of manufacturing equipment. Many of the base machine's components are Library-type parts that will never (or rarely) change, but the final assemblies always contain some customized interchangeable parts like die sets, punches, form tools, grippers, cams, linear slides, levers, etc. that are essentially similar but never exactly alike. A convenient solution is to have complete assemblies of various machines+tooling, with the interchangeable components in place, ready to customize, and use Copy Design on that for each job.
My workaround has always been to keep these template assemblies in regular (non-library) folders, but that can cause frustrating problems with "library" components getting checked out unnecessarily or having lifecycle changes applied when they really shouldn't be.