Stereo Enhanced Mono
It's very doubtful whether it can be done in a satisfactory way that will sound convincing on any program material. Basically you are asking to somehow restore information which has been lost. We can consider various schemes based on splitting the signal into various bands and so on, but the issue is that we are dealing with information sources which do not fall into such bands.

Considering a few "use cases":


solo piano. In a naive way, it might be feasible to divide notes by frequency, keeping the lower octaves left, higher to the right, and mid range in between. As an improvement, we might consider trying to keep a note and its related overtones panned in the same place. (But remember that some strings on a real piano vibrate in sympathy, and here the model might break down.)
A vocal ensemble. If there are (say) two sopranos left and right, it will be almost impossible to recreate what we might have heard on headphones I think. The information is gone.
An orchestra in a semi-reverberant room. The violins are left, celli and basses to the right (noone can hear the violas anyway), and various brass and woodwind somewhere in between. The spectra of the various groups all overlap, and the room reflections add another layer of complexity to the signal. I doubt whether any amount of DSP will do a convincing "mono to stereo" job on this.


It's worth noting that there is one common example of "Stereo synthesised from Mono" which is extremely common; when a multitrack recording, consisting of many (perhaps all) mono sources, is combined to a stereo signal using pan pot circuits. But this is only possible because the mono tracks exist separately to begin with. In other words, information was never lost in the first place, in this scenario, so there is no difficulty in restoring it.