Extracting/ Generating 'side' information from mono recordings?

I realise that mono recordings do not have 'side' information - just 'mid' information. Is there a way when changing a track from mono to fake stereo of extracting/creating side information through synthesizers, manipulating phase shifts, reverb, eq, condensing etc which would allow you to manipulate the (previously) mono recording like a true stereo recording? K-stereo does not seem to create any sort of side info and I am not too sure about other ways that may be possible. I am not very aware of what the relationship between mid and side typically is in good-sounding recordings - I usually just play it by ear.

Any ideas would be really great
David