The transition from mesh-surface to CAD-model is very hard and there are software out there that can do the conversion. Some of them only gives you a "dead" surface (NURBS) model of the stl file. But some even gives you the correct volume that can be edited afterwards. There is some manual process usually, but still beats creating a new solid-file from a STL. The only software i know of and have tried is Geomagic Studio, where I process alot of 3D-scans (mesh files) into STEP/IGES files. Almost always "dead" that is just a bunch of trimmed NURBS-surfaces put together. The more parametric models are still a unknown territory for me, but the software hos support for it.

The only problem is that Geomagic is about 25k USD...