Which of the programs you listed can import and STL, and then export a parasolid or STEP file? Is that even possible?
I use mainly engineering CAD programs such as Unigraphics NX9 and Solidworks, and STL files are useless to me. I need to be able to add mechanical features to models such as blends, chamfers, holes, solid body booleans and etc...
I personally don't know, I've never used STEP files myself. I've only dabbled in the solid modeling side (but 20+ years of working with raw polys...) That being said, my guess would be 'none' : Or some sort of magic would have to happen.
'Solid' files are solid based on the creation of the asset type in the specific software. For example, you create 'a cube' : what you see is a mathematical representation of said cube. It has vertices at its corers (as a result of that maths) you may or may not be able to edit (transform) in your software. When you boolean that with some other solid volume (like a sphere), the results is based on the incoming history combined together: It's all live and editable.
To print that, you turn that solid representation into a triangulated format (that slicers like S3D eat), which in this case is an stl. It's a 'solid stl' simply because the data that generated it was solid. But it no longer has any of the creation history of the previous file format: It's really just a collection of points in space connected by edges and filled with faces. And as you edit the polys, you can make it 'un solid' pretty fast. That's why software like Netfabb Cloud is so handy to heal this stuff up.
I know from playing with Fusion 360 you could import an stl as a 'base feature' (if I remember correctly), so it would exist in your scene as reference with the other solid components: But you couldn't actually do anything to it, since there's no solid model that can represent such an abstract collection of points, that may or may not still be 'really solid'.
But I'm not an expert on the solid modeling side: It's possible someone with far more knowledge may have a solution.
Basically, you start with solid stuff, turn it into polys for printing. To go the other way is not ideal. It's like trying to turn the baked cake back into it's original uncooked ingredients: Cooking your solid model turns it into an STL. You don't have much use for a cooked cake (stl) when preparing another one with different raw ingredients (solid models).
Bots:
Makerbot Replicator 2x / Sailfish on Mightyboard
Custom C-Bot / RepRap Firmware on RADDS
Custom Tevo Little Monster / RepRap Firmware on Duet
You can import STLs into SketchUp for manipulation also. Just need the STL import/export plugin or extension... whatever they call it these days. From experience, 60-80% of the STLs found on Thingiverse can be imported.
Blender can modify STL's but it has a fairly steep learning curve. I am definitely just a beginner using the software. I was recently able to take a STL file for a fan bracket from thingiverse and lengthen it just a little to fit around upgraded fans I put on my printer. I also made two of the walls thinner for a better fit. Took me about an hour to figure it out but my uncle who has been using it for years accomplished the same thing in 30 seconds.